I'm in the same boat as you champ, single since September.
First you need to figure out what YOU want. Do you want to be single or do you want to be in a relationship? I'm guessing you want to be in a relationship to kind of fill that void your girlfriend once possessed. That's not the right thing to base it on and it's going to have you end up scaring girls away, and you are exhibit A.
If you really want a relationship, the best thing to do is take it slow. It sounds like you are jumping into things and when that happens, of course it's going to be a rebound. Taking it slow will help weed out the rebound types while building that base for a solid relationship. Assuming that is what you want.
Waking up next to a beautiful girl,
Step outside and say hello to my beautiful world.