Should I keep stop telling him when other people try to flirt with me?

We've been in a relationship for nearly half a year. A few days ago, someone tried to hit on me and I told them I've a boyfriend. I said that to him and showed him the texts they sent me and what I responded. He fought a lot after that and called me names. He completely distrusted me. Recently again something similar took place and I again told him about it. Now he's cold and distant.

I don't like hiding anything from him. If I don't tell him about these things, my conscience hurts me. So I tell him whenever someone flirts with me. I am making it clear, I've never done anything that would question his trust.

Should I stop that?

Should I keep stop telling him when other people try to flirt with me?
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