I cheated on my now ex bf with a girl, and even though he says that me being with a girl doesn’t bother him, I kept it a secret. He found out because she gave me chlamydia (gross) and I obviously gave it to him. 
I was at work when he texted me a pic of his test results and I immediately denied it, which is silly because the test doesn’t lie. 
He demanded an explanation as to how I contracted the STI and I panicked and told him a fake story about how 2 months ago when we were on a “break,” I met a guy on Instagram and we hooked up. 
It was a complete lie and idk why I told him that, when the truth was, that I slept with a girl while we were together.

Now he’s not sure which story to believe. 
I don’t wanna hear how I’m a terrible person for doing what I did. I already feel awful everyday. 
Why did I do it? Because I wanted to experiment and I’ve always been intrigued by it, and I felt I had to get it out of my system. Not to mention that he was always too busy working, and he had just moved out and I was struggling to adapt to all the changes. 
I only saw her 4 times and after that we hadn’t spoken until after the incident. 
She continues to deny that she has something, even though she was the only person I’d been with so it had to have been her.

Anyways now bear with me..there’s a point to this story. 
I wanna be with him more than anything and we continue to see each other like before, as if nothing happened, except that we’re not technically together. However, I’m not seeing anyone, but he is free to go and find someone else whenever he pleases. I am trying to show him how much I love him and want to be with him. But he says he doesn’t know which story to believe and thinks that I made up the one with the chick. He says he doesn’t care if it was really with a girl because he thinks that’s “hot.”

But every time I try to bring up what happened, or the question of us and if there’s a future there, he gets really really angry and mean, and tells me not to bring it up and starts ignoring my texts and not wanting to spend time with me. He obviously wants to ignore it and pretend that it never happened but inside he is feeling like I played him and that he doesn’t see a future with me. However, if he really believes I wasn’t lying, he would never see me again . 
I’m not sure what to do? Should I let him go and move on or give him more time and be supportive to him? How does a couple move forward after someone cheats and is it possible to be the same?