I would recommend that you go to see your primary care doctor
or your OB GYN doctor about this. I say this because there are at least two possible causes of your symptoms, and the treatments are very different.
First, as you say, it is possible that this is an allergic or sensitivity reaction to the condoms. If so, your doctor should be able to notice some inflammation or irritation of the genitals when they perform a physical examination. Of course, if confirmed, the most important thing will be to avoid this type of condom in the future and, if possible, figure out exactly what the allergic reaction was, something your doctor can help with. Also, depending on how severe the inflammation is, they may give you a topical cream to reduce the symptoms.
However, an alternative explanation is that you may have contracted a urinary tract infection
. Urinary tract infections are a very common complication of sexual intercourse in otherwise healthy young women. Symptoms include the burning sensation with urination that you are currently describing. Your doctor will be able to perform a simple urine test to investigate this possibility and, if you do have an infection, prescribe the necessary antibiotics. Please see your doctor soon about this issue.