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.
1 Allergies - Allergic reactions can lead to leaks in the subcutaneous capillary beds which can cause swelling in the face, including around the eyes.  Skin disorders - Eye puffiness can be a side effect of certain skin disorders, such as dermatitis, if the affected area becomes very sensitive, leading to swelling.