(I'm in high school btw) I just met a guy who I've caught staring and when he overheard someone say my name he turned to look for me. I know the question may be immature, but I don't know what to think. Anyway, do you think he might be interested?

He very well could be.

Now that is impossible to say with just a 'look' in your general direction. No one can even remotely guess if a guy is looking at you because he feels you are 'interesting' or 'special' or 'different than anyone else in the room' .. But, my guess is .. In high school  most guys are generally 'interested' in any female looking in their general direction or shows any level of interest.  You won't know until you talk to him or he talks to you .. So that you can gain enough 'conversational' cues to know for certain if he is genuinely 'interested' in you