In affectionate boyfriend: should I walk away?

Have you ever met a guy who is very reserved in expressing his feelings? I started going out with this guy recently, I knew him as a friend first and he is the nicest person ever, not just to me but to every one around. Very humble and down to earth, always putting peoples need over his. In fact he is best friend (almost like brother) to my cousine. But he is very emotionally guarded, he never talks about his feelings, not just towards me but but to anything. If someone makes him angry, sad no one really knows about it. The only time he is very loving, affectionate etc is when he is typsy or drunk, if we have had a few drinks, he goes on about he likes me, loves me and that he wouldn’t dare date his best friends cousine if he wasn’t serious about us. The next morning when he is sober, it’s like he is juts my buddy all over again. Not much affectionate, or expressing of feelings. He tried to be somehow keeping it cool or keeping it together. We only talk about things we talk about normally through the day like let’s work on this, let’s have lunch, drop me home bla bla, just like the time we were friends.

I am worried that the feeling of insecurity « does he love me, does he love me not » would hurt me. I consistently doubt his feelings. Should I walk away before we go far and mess up everything?