I think the main reason you didnt win was that your king was never safe and it allways gave your opponent counterplay. at the end the position was probably winning for white but taking a long time
I'd like your thoughts

I think that, on principle, you should not offer a draw when you have an extra piece. You should fight for simplification...and remember that, while his passed a-pawn looks threatening, you have the correct bishop with which to cover the promotion square.
I would have played 17. Qxa6 because that way he can't fork you. Also, using the Queen first threatens Qa8+ Nb8 Qxb8+ winning a Knight.
At the end, you have one more piece than he does. I would have done my best to trade pieces if possible and if I couldn't see a way to do it then focus on each pawn with as many pieces as possible and he should have serious problems defending.

I agree with quequeg that after you won a piece you should have brought your king to safety (eg, 16.Nf3 Qb4+ 17.Bd2 Qxb2 18.O-O or 17.O-O-O) rather than immediately entering sharp complications--it's the defender's job to try and complicate things!
I guess you offered a draw because you play with no increment. In OTB chess you typically have a delay or increment so you can finish off such games. I try to play my online chess the same way to reinforce good habits like not offering a draw a piece up. ;)
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Here is a game I played on FICS.
I've annotated the game, explaining all my moves. I'd like to know wether my analysis is correct. I'm pretty sure that I could have won this game but it was drawn, so I'd please also like to know where I went wrong.
Here's the game
EDIT - I'm playing as White.