Yes: a urine test for albumin and a blood test for creatinine. The results of the creatinine blood test should be used to estimate glomerular filtration rate (GFR), which is a measure of your level of kidney function.
Hives and swelling are considered to be different expressions of the same problem. Hives occur mostly on the arms, legs and torso, while swelling occurs around the lips, eyes, hands feet and genitals and can involve the tongue and throat. It is simply that the skin and mucous membranes in different areas swell in different ways. How long the problem has been ongoing is also important.
See an allergist. In brief: No. Allergic reactions to bee stings are characterized by symptoms away from the site of the sting. If all of the reaction to a sting - blisters, swelling, redness - are all directly connected to the site of the sting, it's a large local reaction. If you get stung on the foot and get hives on your arms, or your throat swells or you start to wheeze - those are allergic reactions. See an allergist.