You might have an allergy to latex. Have you tried the condoms that are latex free? You could probably find them on Amazon or something like that. I've heard they are a bit more expensive then latex condoms but it might be worth it to try them.

As for your other problem, you definitely wouldn't be showing symptoms this early. You might be stressed out or have been exposed to bad food. I'd suggest not worrying so much. If your period doesn't come or you feel like taking a pregnancy test you can but wait two weeks from the last time you had sex.

Best of luck.