Oh dear. That's quite a situation you have found yourself in.

Going to the first part about the picture and not being sure if she put it online or not; you don't really have proof. If you were drunk enough to be puking in a toilet; you wouldn't have been totally aware of everything and anyone could have taken the situation. Either way - completely uncool it landed up online and I'm sorry about that.

You need to be careful of how you interact with her. Being sarcastic; regardless of whether or not you had a bad day; will get her back up. Remember - you have no proof she put the pic of you online - so posting an embarrassing screenshot - you may have a lot to answer for tomorrow at school - not just to her - but (a) those who will be repulsed by what you did and (b) her friends and (c) her boyfriend. Sorry to throw that out there; but you've made a complex situation even worse and I think that you need to be aware of that.

What I want to say is this:

You seem to take too little responsibility for your actions.

You got blind drunk because she was with her boyfriend.

Then proceeded to puke in the bathroom.

(put aside the fact that it was posted online - that's a separate issue to you taking responsibility for your actions)

I'm not altogether surprised she's ignored your apology. You crossed the line.

You'll have to give her time and see what happens. Not everyone will be ready to forgive your actions - but if you had a solid relationship prior to this nonsense happening - perhaps there is a chance for the two of you to resume a platonic relationship. I know you like her - but I don't believe at this stage of the game she'd come close to reciprocating your feelings.