Allergy to latex generally causes itching and irritation to the skin, sometimes swelling or hives. If you suspect you're allergic you can be tested by your doctor. You can also try putting on a surgical glove for about an hour and see if you have any reaction on that hand.
My boyfriend and i have been using latex condoms for almost 2 years now and it has been only recently does it hurt after a while and it becomes red and very sensitive to touch. I just found this odd because anything else latex does not bother me.
I would not recommend testing yourself for allergies. Some allergic reactions can be very serious and can cause difficulty breathing and worse. Even if you have not had a serious reaction before, wearing gloves for an hour could put you at risk and you may have a more serious reaction the next time or with longer exposure.
If you suspect you have a serious allergy, you need to be checked under medical supervision. Also, the allergy would not just be to condoms, but any latex material, which is just about everywhere: pencil erasers, rubber gloves (disposable and non-disposable), balooons, shower curtains, Band-Aids, baby bottles, etc.
If you are only having a reaction to condoms, perhaps you are allergic or sensitive to the lubricant that is on the condoms. Try non-lubricated ones and use a water-based one that is hypoallergenic (if you can't find one, PM me and I'll give you the name of the one that I use, but I can't just say it here or I'd be advertising). It could also be that you aren't using enough lubricant or are having sex for too long and that is causing the irritation.