The coolest tactical maneuver, power of the "beeshop"

I thought I overextended my pieces.

Black is totally fine in that position. You are correctly concerned about White’s King becoming another attacker, but if Black moves their Rook to a square that can be protected by the Bishop, there is no real threat of losing an exchange of material. For instance, 27... Re4 28. Kf2 Bxf3.

Yea, I didn't see that in the game.

Nd2 is not a legal move in the position under question, so you must be looking at the initial position. I am answering the question the OP posed within their analysis, which is what to do after 27. Bd2 ...

I guess black has to take the knight with their rook and win an exchange down because they have a horde of pawns.

Black does not have to lose material in the position, so what is the advantage of doing so via 27... Rxf3? Black already has a winning two pawn majority on the queenside. 

Yeah, 27. Bd2 ..., played by the OP’s opponent, was  definitely a mistake that allows 27... Re4 to save the day.