I don't know how to act with my partner

I have a 3 months relationship, it's been a little complicaded since he doesn't like the way I act, but that doesn't care because he told me a million time that he loves me and that is a fact, I know that is true, but it hurts when he tells me that he doesn't like how I behave with other people, when suddenly my attitude changes when I'm with him, he doesn't like that, and I'm glad to know that he has the confidence to tell me what he doesn't like, but I really feel that when he says it he is tactless. When he does things that I don't like, I don't say anything, because then he is repeating that something I told him and that bothers me more. 

I also know that it's because he doesn't want to do something that bothers me, but it really bores and annoys me when he does it, and even more so when he does it in front of other people.

There are things that I know I do because he already told me, but they are so intimate and ultra mine that I can't change them, and every time I do something like that he makes a disappointed face and doesn't talk to me, he looks at me and turns away, and when he's with other people he's completely normal. 

I know that he somehow tries to understand me, but it overwhelms me to know that there is someone behind me who wants to know everything about me, how I am, how I woke up, if I ate well or not, I don't know what to do with the subject of his sudden changes, he becomes so sensitive that any word out of context is bad.

Any recommendations?