What to do? Leave him?

I came back from a hard day of work and wanted to relax on my computer and my boyfriend is staying by me for a while and he uses my computer.
I open my computer and saw he felt his Tagged on and he told me he deleted it a month ago. So I decide since you lied to me and love me so much let me see what why you had to lie about deleting it in the first place.
I checked his messages and I could not believe what I was looking tons of messages with girls that he is flirting with telling them they have a nice ass, asking for their age and actually meeting one of them.
That broke my heart cause we are together for 2 years now and those messages goes back from in the morning to 5 months or more. Lately I have been feeling that he is cheating, going to cheat or thinking about it now I see why with all those messages.
Now I am thinking if I stay I am a fool and I waste two years of my life. I am really really upset and can’t think straight.

What to do?