Checkmate Pattern-Find it!

This is from one of my games. I was losing, but thanks to my oppenent, I managed to find the best move. White plays a3, Black to move! Find the Move!
lichess.org/editor/2b3rk/p4p1p/1p1p4/2rPp3/1Q1pP2q/PR1P3P/1P2B1PK/5R2_b_-_-

Find the move that is NOT Qg3

Uhhh.. Qg3 lol

What about Rxg2, I can't see a way for white to defend it after Qxh3

Qg3+, Qxg2#

Qg3+, Kh1 or Kg1, Qxg2#