He is sensitive and has low self esteem issues. And you got into an argument with him while you were drunk, while using WhatsApp. If you KNOW he is sensitive and has low self esteem issues, you really shouldn't do that stuff.
When people talk with one another, body language is involved. It's how you interpret the context in which a remark is made. With WhatsApp that's missing, and that leaves the interpretation of messages send back and forth sometimes wide open.
So odds are he read something the wrong way and got upset about it. Next day you apologize, but he's still pissed off I guess. Then, eventually, he lets it go and accepts your apology. (btw, this is just a hypothetical interpretation of his feelings of course).
And perhaps being blocked on WhatsApp is a good thing, since it seems to me that talking on WhatsApp started this mess. Call him, or better yet, pay him a visit.
I wouldn't move on though, certainly not since I feel that half of the blame can be squarely put on your shoulders.