38,fxe6 fxe6 39.Rg1 was worth considering.

It doesn't save the f-pawn, but it does setup a great opportunity after 40.Bxf5 to up the pressure on you with 40.Rc4!

Black misses his chance for 40...Rc4, but all is not lost yet.

actually no to Rh8. Your king is suddenly in grave danger again here.

black slows the attack with 44...b4 44...Rdb1+ and the danger to white is strong and very real.

45....Rgb1+ is still strong, but black fails to play this for example 45...Rgb1+ 46.Kc2 b3+

For a speed game, you played reasonably well in some very complex positions. A combative game. For analysis, go through the variations more completely. Analysis is the search for truth, not just an affirmation of how well we play. To improve, I always search for my mistakes even harder than I look for my opponents mistakes. In speed chess, the initiative is everything. Always play for the attack as much as you can.