This is probably not an uncommon problem among younger male youth leaders. It has happened to me a couple of times, and it always is terribly awkward. A couple bits of advice: on the one hand, try not to let on how awkward it is and try to treat the girl as normally as you can given the situation. On the other hand, as you indicated, it can be a sticky situation, so protect yourself. You really should never spend time alone with female youths anyway, but in these situations, you should exercise even more caution in being alone with the student. Just in case an accusation comes up, it's always best if there is another adult that can attest to the appropriateness of your conduct with the student.
In one of the cases where I encountered this type of situation, I talked to my wife about it (I think she was still my fiancee at the time), and tried to make sure she was present anytime the student would talk to me outside of youth group. In this situation, the student was sharing deeply personal struggles with me that was better suited for same-sex mentor/mentee type relationship. Since my wife was there to hear most of what she shared, she was able to take on part of that relationship with the student. I also encouraged the student to share with her small group leader. As a result, my wife and, to a lesser extent, her small group leader (a woman) became the people that she turned to with her issues. Thus, in the end, even though it started out as an uncomfortable "crush" kind of situation, it turned out that what she was really looking for a someone to listen to her and show her compassion and love. Since then, she has gotten much better at turning to same-sex adults and her peers for the kind of attention that she needs, but she and I are still comfortable with each other, because nobody ever made a big deal out of it.
That is just one example, and each case is different. The point is to let the Spirit guide you in determining what the student is really looking for. (Sometimes is it just a silly crush; sometimes there is a deeper need that is expressing itself in an inappropriate way). But, in all cases, don't make a huge deal out of it, but be smart about your interactions with the student.
I hope this helps.