Am i wrong not trusting my boyfriend?how can i overcome my fear?

he has been an alcoholic since he was 14.he is now 28,n sober for 6months now.im 18.been dating for 2months.he has been amazing to me.hasnt given me a reason not to trust him.he has done so much to prove to me he wants to be with me.he talkd to my mom.disapproval didnt stop us.he got me a phone.last mnth when i was 17 my mom found out i lost it to him n wanted to put him in jail.he didnt ran away instead he stepped up n said he wants to be with me and will take consequences.on tuesday he lost his mind.he said if i didnt give it to him he will get it in with someone else.i broke up with him for saying that.that night he tlkd to another girl.he didnt want to get back with me.the next morning he actd like nothing happend.we then met up to tlk.lookd like he wantd to cry but tried hiding it.when i askd him what he wanted his tears ran down n he said he didnt want to lose me n he lost his way of thinking tht night n said stupid things.i knw the person he was tht night was not the person i know.it doesnt make sence to me.but im now having trouble trusting him because of the msgs i saw of tht other girl.once we talked things through i havnt seen another msg.he said he just wanted a replacement but its me who he wants.inever go through his phone or anything becuase i trusted him.i felt stupid going through it and not finding anything yesterday.im just scared that now tht we got back together he still might be talking to her.ineed help overcoming my fear.iwant things to be like before when i could trust him.please help!!!