Yes, it is possible to get an STD through strictly oral sex. One possible STD is herpes. A person with herpes does not always have the warts associated. They could just be carrying the virus.
Let's assume that she has herpes. If she didn't have warts, she still carries the virus. The virus only needs a microscopic scratch or cut on your penis to travel from her saliva into your bloodstream. The presence of warts extremely heightens these chances. And since a person can be a carrier without knowing it, yes, you could be infected even if it was a year ago. (This scenerio is only ASSUMING that your partner DOES have herpes.)
Hope this helps!