He cheated on me and I don’t know what to do anymore. Please no rude comments!

So my boyfriend and I have been together for about 2 years and we live together. I found out a few months ago that he was cheating on me. He was paying for sex. Even tho he cut me off from sex and wouldn’t be sexual in any way with me all of a sudden. He said he did it because a couple times that we had sex I said it hurt (he will not do any foreplay to me at all) I decided that we could try and work things out since we have a signed lease together that isn’t up until spring. I feel like I’m lacking so much from him. I’m lacking physical touch, and him just being there emotionally. He swears he is but he just isn’t. Anytime we make plans he will make different plans and say that we can just do what we planned another time. He NEVER initiates sex, ever. I always have to. We can go months without sex if I don’t initiate it. I’m just craving someone to want me. Physically, emotionally, anything! Just someone to cuddle with me because if I want to cuddle I have to initiate it or we won’t cuddle. And when we do, he’s not an active cuddler. I basically just lay my head on him and he doesn’t even put his arm around me or anything. Ive talked to him so many times about this I’m just exhausted and don’t want to talk anymore. Even if I do he gets annoyed and says he’s tired of me repeating myself so I’ve just stopped talking about it. Anytime we drink or anything together he makes me feel so self conscious for even speaking. He tells me I’m being to much right now even if I’m just trying to have a conversation deeper than “how was work”. We can’t break up yet as we share a one bedroom apartment and to break the lease is $7k and I don’t have that money. I just want to cheat on him at this point just for some kind of peace of mind that I’m still wanted and beautiful and men still find me attractive. I feel so worthless. I know cheating is not a good option but I just feel so lonely. I don’t have any family or anything so I don’t know what to do. He says he loves me and I’m the only woman he’s ever wanted to marry or even seen a future with. Idk 😔 should I go out with someone new that doesn’t want anything serious until my lease is up?