Boyfriend help .~_~. not sure what to do wrongfully accused ...?

Ive dated my bf on n off 3 yrs im 22 n he's 29 1st time we split cuz he was having a baby on the way n was conceived while we were dating so i couldn't get over it we split up n i went back to my x he consider this cheating mind u we weren't 2gether i found out my x was cheating again n left stood by my self for a while we found our way back to each other n i excepted the fact that he is having a child from sum1 else since he excepted my daughter when we 1st met so we tried working it out went good we had our ups and downs n in our argument today we had over disapling my daughter cuz she didn't wanna take a nap i prefer to do the talking and disciplining he was giving me his advice n he got upset cuz i didn't wanna take it (no we do not live 2gether) we had argument cuz he says im letting her walk all over me mid u shes 3 his son will b one this month so i get mad stop talking to him he told me we were over so i change my status to Single it post on fb n my drunken friend decided to post well why don't u come out to hav a drink with me my bf sees that on fb n write wow drunk friends says y don't u go out with name which happens to b my old coworker/ his cousin which my bf always suspected that we were intamint due to us only being friends nothing more , which of course my bf read n told drunken friend o really ty 4 telling me drunken friend says wat does that mean i notice the convo n type wtf r u talking about drunken friends name drunken friends says oh my bad im drunk don't listen to me so bf now believes im cheating on him with friend i spoke to my friend told him plz tell ur cuz to stop typing bf n me fighting n we broke up friend that bf thinks i'm cheating with ask me wa can he do to convince him we r Just friends plz help not sure what to do ive tryed talking to him he wont believe me