Do I give up ? ?

I have been on and off with this one guy for 3 years (we have broken up right now though) and I really want to get over him but I can't he's the sweetest person and he makes me happy when we are actually in a relationship,  I want to move on with my life but i don't know if I should since there might still be something there between us , Everytime I see him talking to other girls I get a little jealous I just feel like he doesn't care anymore or he might just be acting like he doesn't care , All I want to know is should I move on? Does that seem like a good idea?