C.M.
I've been there. Terrible twos. I don't really know what to tell you except be firm with her. Time out for bad behavior is in her room, period. If you're out use a stroller or shopping cart so you don't have to carry her. I used to lock myself in the bathroom for a moment of sanity. It helped, even with him banging on the door. As far as the gagging, my son did this too. Once he made himself throw up and I didn't react he realized he didn't like it and stopped.
I wish I had more to tell you. All kids go through some form of this and it does pass. Then they hit troublesome threes where they want to be on top of yu except when you need them near you and they want to run away. Hang in there. When all else fails get a babysitter just for a few hours and go out for coffee all by yourself with a good book. Take a bath while she naps. Take time out for you. It helps.