What choice do I make and am I wrong

It is our year and a half anniversary today. Today I wanted to sit him down and tell him we should split up.

Early in our relationship, he constantly was messaging girls, asking them to come over when I was at work, telling them he was single, commenting on these girls bodies and how hot they were. And I found all the messages from multiple girls eventually. I still check his phone because that's the woman I have become. That lasted from being 4 months in to about 3 months ago. I check his phone now and can't find anything, thinking yeah maybe he's really trying or he's hiding it really good. But, 2 weeks ago I found a girl on his recently-talked-to friends on this app, and he lied to me about it. A girl he used to hook up with. And since then I've been ready to start moving on. Only problem with that is that he lives in my house and helps me with bills. I haven't run out of love for him, but I know he doesn't reciprocate the same amount. His mind is elsewhere. He doesn't want to do anything with me. I just wish I could do it and start treating myself better. With that being said... please give me your advice. Do I work on it or should I start something else?