It may not look like it, but White has a forced win here! However, you have to find very concrete moves all the way to mate.
If you didn’t see the key non-checking move, then that did you in.
1.Qe7+ Qg5 [1...g5 2.Qe1+ Qg3+ 3.Qxg3#]2.Qe4+ Qg4 3.Qe3 And here is that move! 3… g5 [3...Qg5 4.Qh3#] 4.Qe1+ Qg3+ 5.Qxg3#