Is it normal to be horny while holding hands with my girlfriend?

This is my first ever girlfriend, and I'm 16, and we were holding hands in the mall, and pretty much the WHOLE time, I had a bone r...but I obviously hid it, my shirt over it, but the whole time..then in the ride back to her house in the car, she had her head on my shoulder and my head on her head, and i had a bone r the whole ride... is this normal at first? Will this be every time I be with her, or just now, because I'm new?