How to break up with Histrionic Partner

The next day after we broke up (or atleast I thought that I did) I got text from him as if nothing had happened the previous day. I tried to tell him how its not making any sense and how I cannot continue this anymore. But he wouldnt listen, he says we have to make this work for and says he will work on the issues and doesnt let me go at all.

Its been two weeks since and I have not met him but we talk over the phone, he talks as if nothing has happened, we never broke up. but its all different, it all seems fake. I cant exactly point out what it is but everything he does now seems superficial as though he is trying to put up an act and I don't know how to act like that so it got weirder.
I tried to tell him to be honest with his feelings and he doesn't have to be nice to me if he doesnt feel like after our fight. he says what fight?

He continues to lie to me and I know he is lying but i cant prove it and its very frustrating. I spend a lot of my time thinking about how to catch his lies with proof and show it to him.. Its not like I dont know that he will not accept anything and nothing changes but these thoughts are making me miserable and almost nonfunctional. I'm now obsessed with proving to him that he is lying. Its exhausting. I live in a confused state of mind now and I'm not able to perform well in my job or follow my routine, I'm so stressed out that my head weighs a hundred pounds all the time. All my time is spent on useless thoughts.

I figured the only way for me to get out of this is to get him out of my life.

I read a lot about different personalities in these weeks and found out that the only way to break up with him is to go no contact. So today, I've deleted his number and going no contact with him. Hope I get through this.