Allergic to Condoms??

Please help!! Is it possible to be allergic to condoms without having a latex allergy?? 
Background: Almost every time I have sex (always with a condom), I get this awful, intense tingly-burning sensation similar to having to pee. I usually end up trying to pee three or four times to have barely anything come out. When I do pee, the feeling usually gets stronger and worse!! I know I'm not allergic to latex. We started using lube a while ago and the feeling died down some, but is still very noticeable. I really hate that this feeling always ruins sex for me!