If I was young, I might have been immature and showed it to friends. However, even when I was young, I know that I would have cherished the letter and kept it even to this day even if I was not really interested in the girl. I would have definitely talked to her in private at some point although, being young, I might have been scared a bit (I was not very brave when it came to girls when I was in high school).
Given my 53-year old (more confident and experienced) personality in the body of a teenager though, again, I would cherish the letter and I would seek out the girl to talk to her more about it in private. We didn't have cell phones when I was a kid, so we would actually have to go up and talk to the person, but, today, I guess I would first text her if I knew her number or ask a girlfriend of hers for her number. In that text, I'd invite her to talk, in person, somewhere in private and take it from there.