He probably did have them to begin with, actually. They can hide for a while and show up at random times. You need to start using protection and see the doc because you will get HPV from him... if you don't have it already, go get the vaccination.
HPV is a virus- certain strains of it cause genital warts, and certain strains of it cause cervical cancer in women.
If you see your doctor now and make sure you get tested and taken care of, there are medications you can take to prevent yourself from catching it from him. If you take control now, you probably won't experience any serious side effects (including fertility or cancer).
Use protection, and do NOT have sex with him while he has warts, even when you're using protection.