Should I move on past my ex?

So about four days ago my ex fiancee of six years and I split up. I decided to move 12 hours away with my child to clear my head. The break up was me thinking he was cheating and pulling away from me and him saying for two months he had thought long and hard and said he hadn't loved me in two years and it would be best for me to leave. He said by leaving our negative environment wouldn't affect our ten month old baby.a couple days Later however he said the break was bc I couldn't be patient enough to leave him be ie give him enough space, not push him and nag him and just be patient for him to work for his promotion. He let me take our daughter away as well without a fight. He also told me that he never thought we could be together again however I ask him in maybe a couple months if we could reconcile once we have had space he tells me he doesn't know bc two months is a long time. Aother big issue we had was about two months ago he started texting this girl all the time and I found out through a phone bill. I asked him to stop but he said he's a grown *** man and does what he wants and I need to trust him. The issue escalated when one night he went out and I saw call records showing he was texting her non stop and then they stopped so I assumed he was with her and cheated on me. Later on I felt like a horses *** bc I found out he never cheated I was just making up my theories. My question is do you think space might heal this? Why is he still texting this girl all the time and what could she mean to him? This girl lives in a city he will leave shortly for a promotion so I don't think he's looking for long term with her. If I do no contact with him other than discussing his daughter will he change his mind? It'd hard bc he will say something like I won't change my mind and then says he wants to keep in contact and he even texted me the other day to tell me about his job promotion which isn't relevant to me since we are broken up. I just get confused bc he says he doesn't want me yet he texted me to make sure we got to our destination okay and is worried about us. So, should I give him a couple months to figure out what we both want? Or should I move on bc all signs are pointing to an end? Also we have broken up once before and within a month and a half we were back on bc we missed each other so much. I just feel that if he didn't have some feelings left he wouldn't even bother talking to me at all. I think just how difficult it has been lately is why he said those things or could it be an influence of this new girl? Please respond....I want my family back so bad but don't want to sit around waiting for him if I don't have a chance.