I had sex for the first time and about a week after my labia majora around my hole turned red and itchy. I have two questions: 1. can this be an allergic reaction if symptoms occurred that long after? and 2. The condoms were lubricated, so how can I know if this is a latex allergy or a lube allergy? I have never had problems with latex gloves before.

Maybe you should consult to the doctor because they only know what kind of allergy that you have...

It doesn't sound like an allergy. An allergy wouldn't occur a week after the incident. You'd know immediately.

This sounds like either an irritation, or an infection. Best to see your doctor to have it diagnosed accurately.