Well there you were forced to give up the queen. However, the resulting material imbalance should be good for you...ok you are down a pawn but 2 bishops + a knight should be better than a queen. As a general rule when thinking about exchanges it is usually the side with more pieces which stands better eg.3 minors vs Queen, 2 rooks vs Queen, 2 minors vs rook. It depends on the specific position of course, but usually the stronger piece cannot achieve as much alone as the weaker pieces can achieve working together.
On move 13 I would be concerned about white playing Be3 and my queen running out of squares. I think 11.Bd6 was the move which made things awkward, with this you are no longer able to drop the queen back Qd7. Anyway, as I say you were already up a piece at this point and even though white could win your queen for 2 minors the position was still good for you.
So, how can you prepare to play games like this without the queen? As a side question, what should you be thinking on move 13? I thought I should develop the knight. Why didn't it work this time?