The slang キレる means "to be mad", or "to get pissed", while 逆ギレ would quite literally mean "to be angry back at someone who should normally be the one angry", where the person at fault is the one being angry.
The こっち part would mean "here", it implies "me" or "I". The が after is simply pointing towards "who" specifically it is that should be angry.
You might also be familiar with the expression:「それはこっちのセリフ！」"That's my line!". The こっち serves the exact same function here.
So, to put it back in context, the sentence would read:
A: "What did you just say!? I came to wake you up and now you're mad at me? I should be the one angry!" (A is pissed at B for not being grateful)
To learn more about where キレる came from, read this post too: Where does the word キレる come from?