 need to go to the doctor, but even if it comes to that you’re fine, you both were playing and he knows that, unless he’s an immature brat but even in that case it’s still not your fault, so relax and just make sure not to joke about it too some, give him a couple of days before that.
I once did something similar and lived to tell the tale.
I like doing weird shit, like holding doors open (usually at Wawas) for men and bringing special ones flowers.
So, a few years ago, I was out grocery shopping.  
I get home and eeeeeverybody is home. (In others words, abut 6 or 7 people witnessed this... gawd help me living it down.) I grabbed a bag of groceries and the flowers. I put the bag on my forearm and had the flowers in my hand. I get the brilliant idea to hide the flowers behind my back and the bag goes with them.
I walked up to Bud and pulled my hand out from behind me and presented the flowers to him. As I did that, the bag containing 10 huge navel oranges came flying out too and whacked him in the cajones.
Well, I died of embarrassment and everybody fell on the floor laughing and he went from starting to say what sounded like, "Oh, cool..." to "Ohhhooooooo" accompanied by a little hop backwards, which was hard to pull off as he was standing with his back against the counter to begin with.
Of course, this is a man who once set green grass on fire with a rheostat so the concept of innocent human activities going to hell in a hand basket isn't foreign to him. At all.
I got hit in the nuts HARD with a closed fist once and the pain was probably an 8/10 for maybe 5 minutes, which seems long at the time, but really wasn't. You didn't mean to, so the dude overreacted with sending you home. If he holds this over your head (heh) or psychologically punishes you, tell him to sack up.
Dude gets hit in the nuts, hard, better believe he’s allowed to ask WHOEVER did it to leave while he chills out.
Don’t use an anecdotal example to show why he is “overreacting”.
Meh, don't agree with you at all. I'm okay with it staying like that.
Definitely look into it if it doesnt stop hurting. Testicular torsion is real, I knew a guy who racked himself longboarding, waited a week to go to the hospital and had to have his removed.
It was an accident. He's upset now, but I'm sure he will get over it. I have absolutely accidentally hit my husband in the balls with stuff before and he always gets mad but then recognizes that it was an accident. 
It will totally be ok.
I mean if he's being reasonable, than he knows that rough housing, things can go wrong and accidents can happen. He was probably just still in a bit of pain, feeling upset, overwhelmed but didn't want to be mean or rude. I get that, if that's the case.. there's been times I'm upset, or in a bad mood and I know it's better to just not be around my g.f at the time because I do care about her, and I don't want to say anything stupid, or be rude because I'm not feeling well. So he probably just wanted to take some space and chill out, while making sure he didn't do something mean because he was hurting or feeling embarrassed.
Aww bless him, and you. Accidents happen. I'd maybe text him the next day to see if he's ok or maybe do a door drop and run with a pack of beers or his favourite snacks in a bag, and a little note.

Yeah honestly if it was an accident I really wouldn't worry to much. Whenever me and my bf are play fighting if I accidently get hurt and if it really hurts and he tries to comfort me I tell him not to touch me and I don't mean it in a mean way I'm just overwhelmed. I still love him though.
So for the most part, it sounds like he's really milking this or is a super super sensitive guy. Source: Am a guy, know lots of guys. We've all been hit there many times.  If this is abnormal "getting hit in the balls" pain to him, you need to tell him he's going to the hospital to get checked out and help him get there. I knew a guy who's brother whipped him in a public shower with a towel. It literally unraveled one of his inside of the sack and he lost it. This is possible unfortunately but is fairly unlikely. The odds of hitting it just right, with just the right angle and with just enough force, and his skin to be just the right thickness and his ball in just the right position, is extremely unlikely. More so and near impossible with a hand through clothing. If he's eating anything with a lot of hormones in it, it could effect his sensitivity, but mainly emotional. If the pain stops, I would consider his response a red flag. He very easily could have been pushing your feelings to the side and purposely trying to make you feel bad for attention or favors. I'm not saying that's what it is at all and I'm not going to get into your relationship. I'm just saying this isn't normal and being a guy, knowing so many guys, manipulative ones and good ones, it doesn't look good from my perspective.
Echoing some other comments it was definitely extremely painful but at the end of the day if you just apologize and say it was an accident then youll be fine. Getting hit in the nuts hurts like hell but you get over it.
He is probably embarrassed. Unless hes the cry in front of you kind of guy, hes not comfortable with how you saw him. 
 I wager he asked you to leave because he was repressing an urge to strike you, Dont get me wrong, a good man will never hit a weaker person out of anger, not unless attacked and in danger, even then with restraint, but the primal urge to throw a left hook at a person who just hit you in a way that disabled you is there for most people.
Guys always have stories about being hit this way, and something always comes to mind because we find out for the first time that we need to be careful about this when we are very young, and it gets exploited in ways that make us a bit touchy about it. especially if he has ever been laughed at over an incident involving it.
So, that's the understanding part...For the solution I would try the following approach...
Express that you didn't mean to hit him and if he would prefer, it will never come up again. I would tell him you feel bad but understand that it can be embarrassing, and you aren't judging him, it was an accident and hurting him was not something you meant to do. I would give him the message you don't want to add insult to injury by teasing him, and you certainly dont want it to be more than a momentary accident and to ruin anything because you care and you feel terrible already.
Then I would ask if there is anything he would like, like to say, or wants to do that would help him out in feeling better about it.
When he says no, and he will almost certainly say no, tell him that you would at least like to make dinner or the like and when you show up, make/ bring food, look around, and knock out some chores a person with a sore walk might have trouble with.
Then find something to watch, and cuddle some...recognize sex is probably going to be a couple of weeks or more if he has a bruise. 
If he doesn't bring it up, don't mention the rage thing...he doesn't want to tell you about it if hes a good guy. He feels really bad for what went through his head and that is a mixed bag for a man trying to be good to a woman but having the impulse to act violently. its hard to get comfortable with...a reminder that you are there and theres more to you than what it sticking out in his head is needed at the moment....
or, hes like me...and you will see him next and he will cover his balls and yell "dont hit me" and laugh when your face turns red...And that will be the end of it...until he fucks with you about it for fun again later...in which case this is going to be easy, so most of this post is for if it's not...
I would check up with him and ask him if hes still feeling pain and if so maybe to go to the hospital to see if everythings all right?
Aside from that...Apologize and just be honest that you didnt mean for that to happen.

It was an accident. You both were playing around and usually when that happens it doesn't stop until someone gets hurt. Outside of a sincere apology it should be over.  Guys sometimes exaggerate things. My husband is this way. I accidentally poured luke warm coffee on his arm, and it surprised him so he screamed... made it seem way worse than it was. Later that day he slapped my badly burned skin and I just kind of held my breathe to keep from screaming since it hurt and moved on. He still brings up the coffee thing, until I remind him of what he did and how differently we reacted. It really should be over by now.
As a male, I can feel this post...
It'll be fine. My girlfriend and I were having a