Is it possible to be allergic to sperm and lube, do brands use the same lube on all their condoms

When my boyfriend and i first started having sex it would burn but I thought it was normal it being my first time. After a while I realized that the pain went awAy but it would still burn and by then we tried 3 diffrent types of durex condoms so I came to the conclusion I might be allergic to latex since I have heard of latex allergies. We tried using "skyn" a non latex condom by lifestyle which worked fine for me but unfortunately the condom only came in 1 size and is to small for my boyfriend. So we tried using "bare" another non latex condom but it would burn extremely bad. So I came to the conclusion that I'm allergic to the lube on the condoms which happened to be by the same brand we used in the beginning the brand "durex". Now when we have sex without a condom it burns as well but only when he ejaculates. This whole allergy thing has made sex very difficult
Honestly I was wondering am I the only one that this has happened to.... And can you be allergic to both?
Don't know what I'm suppose to do and do they have medication for these kind of allergies?
Would brands use the same type of lube base for all their different condoms?
And if any1 has had this kind of problem what type of condoms would you recommend?
The pain has left me scared to try new condoms