I'm upset about my ex dating others while living with me
That's messed up. Why does she still live with you and how do you feel about her dating others?
It's humiliating for me, and she's still here because we're waiting for one of us to find a new place to live.
Ending a relationship is hard but it is not good to want to control whether your ex dates or not. Especially if you don't care about them anymore. People will think you are selfish.
She thinks that she's so great just because she's dating, and I don't want to date anyone else right now.
Well, if you won't date anyone then it is your right to do so but it is also her right to date whoever she wants. Maybe you can move out or let your ex move out so that you don't get overwhelmed whenever you see her together the person she is dating. I think it will be healthier for you to do that.