Search Results: move out from boyfriend''s house

So, some context. My boyfriend and I were together for almost 3 years. We moved to another state together, and we had been living together for the last year. There were a lot of things coming in between our relationship, like how we were living with my mom (awk, I know, things were complicated and we couldn't afford to live on our own yet), we didn't have the same days off so we hardly saw each other, etc. It got to the point where he only wanted me around for sex in exchange for him doing things for me like cooking dinner or driving me to work which was down the street. It didn't feel like we were a couple anymore.

About a month ago, my coworker was worried about my well-being and expressed how he always thought I was pretty and how he wanted the best for me, and it was nice hearing that from somebody at the time. I ended up inviting him over to the house while my boyfriend was at work and we did sexual things. My boyfriend ended up finding out what happened after looking through my phone and I was trying to explain why I felt the need to do that, but he wasn't believing me. I broke his trust. I owned up to what I did but he was too hurt and has been hurting ever since and it kills me. I've started therapy and got an STD test which came back negative, and I'm working on myself to become a better person, but I feel like it's too late since he already closed his heart off to me.

TLDR: I cheated with my boyfriend of 3 years and he doesn't trust me and doesn't want to take me back. I'm having trouble moving on because he was my everything.

What should I do? Should I keep trying to fix our relationship? How can I prove to him that I've changed and I won't ever do what I did to him again after going through the pain of losing him? How can I get him to trust me again? If you've been cheated on, did you work things out with your partner? I still feel like a shitty human being, but I'm trying to fix what I did wrong.. any help or advice would be appreciated. :(

Me and my ex were together for just over a year and practically living together. We did a lot together - he helped me lose weight, get my drivers licence, and came with me to doctors appointments. We did a lot of firsts together and had/ have a great connection.
He went to jail for 3 months and I waited for him and he was appreciative and happy and was calling me everyday telling me he loves me and was talking about making future plans - we were getting serious and his mom even invited me over for Jewish Passover holiday. Now during the month of June we had quite a few fights over stupid stuff like what I should wear when we go out, my diet and I was also getting irritated when he was on his phone a lot and he was getting overly sensitive anytime I wanted to go back to my house for 3 days and then come back to him. He was scared of me leaving him and he also felt unappreciated , but I always showed him I cared for him - like going to the hospital everyday when he had surgery. Now he starts dating someone who is totally the opposite of me exactly 2 days after we broke up and after 3 weeks they are saying “I love you” to each other. But he says he still wants to work stufff out & possibly get back together. He still kisses me and has me sleeping over at his place during the week and only sees this girl on weekends, but he tells me he doesn’t have history with her like he does with me... and says he needs time and doesn’t prefer her over me right now and that it depends on me and doesn’t know what he wants to do. She’s a dark gothic girl and he’s a classy type of a guy who wears suits and likes to be well dressed and she’s way taller than him and is the total opposite of me - I’m sweet and sensitive, she’s the psycho angry aggressive type and dresses like a punk rocker - totally different from me!
Also it moved very quick - after 3 or 4 weeks saying that they are in love?
Is he in a rebound relationship? And is there a chance for me and him to be back together?