oh, i don't really know what to say!!
when i read the part about making her run laps, i had a reaction. not exactly sure why, but i think it's because it seems over the top to me. #1: would this be humiliating? it would be for me, and that is shaming someone. not good in my book. #2: would it be effective? i think you need to examine your motivation a little more, and just sit with this for a day or so.
#3: could you and girl have a private talk after practice tomorrow? as you have said, there is nothing you can really do about it if she does indeed have a problem. but if you want to send her the message that you care, you can do so in this way. if you want to let her know that making inappropriate comments on fb is unacceptable, then let her know what the consequences of continuing it could be (expulsion from the team?)
if you want to let her know that she, as an older teen, is a role model for the young upcoming ones, i think that's valid.
good luck with your decisions.