No, for a couple of reasons.
First, you are both virgins. If neither of you have done anything with anyone else, neither one of you could have an STD. If you don't have an STD, you can't transmit one.
Think of it like a cold. If you get a cold, you've been exposed to it somehow. You've had to have been around someone, somewhere, who had one for you to get it. It just doesn't develop in your body - you got the germ that causes it from someone else who had it.
STDs are the same way. You have to have sexual contact of some kind with someone who has it to get one.
Second, fingering doesn't transmit STDs.
The only ways STDs are transmitted are by oral sex - that's when someone's mouth is on someone else's genitals (think blow jobs), or by genital to genital contact - this can be rubbing or grinding without any clothes on, or intercourse. This also includes anal contact - either mouth to anal, or genital to anal.
Something to note - if either one of you has oral herpes (cold sores), you can transmit that during oral sex, even if a cold sore isn't present. Cold sores are caused by herpes simplex virus type 1, or hsv1, and if someone gets that genitally from oral sex, it would become genital herpes type 1, or ghsv1.
It's awesome that you are asking questions and getting this information before doing anything. :)