My boyfriend's penis itches after we have sex without a condom. Could I have an STD, or is there something else going on with my vagina that could be causing the itching?
Some couples have an "allergy" to each other in the sense that skin-to-skin sexual contact can cause some sensitivity and antigen issues. You could also have undiagnosed vaginitis or other condition that is currently asymptomatic that is causing the reaction. For your own health (and his!) and for your peace of mind, both of you should get checked out by a doctor, just to be sure there isn't something going on that requires treatment.
In the meantime, I would strongly recomment that you use a condom for STD prevention and to prevent pregnancy. It will also have the added benefit of keeping the itching at bay after intercourse while you find out what's behind the problem.
Here are some articles you might find useful:
Myths about Sexually Transmitted Diseases (STDs)
10 Things You Need to Know About STDs
10 Tips for Men’s Sexual Health