Is this endgame winning?

I played this game yesterday in an important match which my team won with 5-3, meaning we are safe in the Dutch national competition. After a while I won a piece, but the endgame that followed was very hard to win. In fact, I used up nearly an hour of my time to find a winning plan, and the best I found was a trap my opponent luckily walked into..

The position after 28. a4 is my problem. The plan I used in the game was to attack both f2 and a4 at the same time, and got this tactical opportunity to exchange queens.

The other plan was to advance my kingside pawns, but that seemed very dangerous to me. Thoughts?

I really really like 36...b5! You're definitely winning after 35.Qa8? I must say that this is very difficult endgame, you did very well. My intuition says it is winning...

yeah this endgame is winning, but it can be very difficult to win.

Really? Silly me, I thought it was dead easy to win. In this case, white is going DOWN the board. All Black needs to do is push his f-pawn and win. There really isn't anything difficult about it.

i never said it was difficult, i said it can be difficult, if you let white in, trickery sir.

I looked at 36. ... b5, if 37. a5 yes I agree, it is easy. But I thought white had 37. Qc6. Thought I'd simply lose the pawn there.