It sounds like you have all the answers at hand.

He drinks.

You do not know what he is like when he is sober.

He has an addiction that takes him away from you.

Your needs are not met.

You cannot relate healthily with each other because the drinking and the bar visits stand in the way.

He does not recongnise all this.

You struggle to continue.

What to do?

Talk to him quietly about him, when he does not drink. If he is willing to look within - great. If not - move on. You have been with him 3 months. Thats a good time to let go if things are not right. I have been with someone who drinks every night for 7 years. His drinking only got worse and he got abusive. I left. Cut your losses and maintain your standards. Good luck!