how do I fix the bite monster?

I cannot figure this out, I have tried several different ways of trying to get C to stop biting, but it is NOT WORKING! I took him to the mall today to play, and he was doing fine, until he saw Balloons.
He LOVES balloons, so he started going towards them, some Mary Kay rep was bugging me about a makeover, and I politely told her (several times) that I am kind of busy with a kid nowadays (I should have told her to PISS OFF). By the time I finally shook her, he was at the balloon, and he was playing with it. I wouldn't have had a problem with this, but it wasn't his balloon to play with, so I took him away from it to the other side of the play area, and he went straight back to it. So I took him away and he threw a shit fit!
I took him out of the play place to calm him down, and he bit my arm, HARD. There is now a mark with a small bruise from where he chomped down. Of course being in public I couldn't give him a spanking (because I don't want other parents calling the spank police). The "No biting" technique didn't work, and because we were at the mall I couldn't just set him down and walk away! I put him in his stroller, but he didn't cry, he just chilled out like "what did I do?".
So now I'm faced with the question of How do I tame the bite monster? Although sometimes It's not just the biting, sometimes he pinches and hits, WHAT DO I DO!!!! I've told him no hitting/pinching/biting, and he laughs. Spankings haven't worked, and if I do it back to him, he will think it's ok to do it.

Right now, I feel like I'm S.O.L