white assisted you by missing a better response 2. Qxc2 losses immediately. He could have strung it out longer by playing 2. Rxf7+ Kxf7 3. Qd5+ Kf8 4. Qd6+ Be7 5.Qf4+ Kg
8 6.Qb8+ kh7 7. Qb4 and more. You could have run out of time before mate on this route. You did well, but you got lucky too.
My continuation went 7. ... Qxg2+ 8. Kf4 Qg5+ 9. Ke4 Qf5 10. Ke3 Qe5+ 11. Kd3 Qe2+ 12. Kd4 Bf6+ Kd5 13. Qe5# there are a few other lines possible, but this is the one I came up with.
I encountered the following position in a 10 minute game. At the time this position was reached, my opponent had about 3 minutes left to my 25 seconds. I had to come up with the winning combination quickly. See if you can see how I continued. Or tell me if you see something else. Enjoy!