He is an abusive drinker, he abuses alcohol and he then abuses you in the process. A careless drinker had one too many one night, had a bad hangover, said "not doing that again" and didn't do it again.
No one deserves to be worrying, do you see how his life is consuming you? See how you are living in fear that saying the wrong thing could trigger his anger?
I know that this side of him is unhealthy for me, but the other side of him is so great. He is the sweetest and most patient and gentle person in my life. He seems so normal when he isn't drinking. I don't know how to proceed? I want to help him so that we can be happy together. Can we ever be truly happy worry free?
That's what alcoholics do, they are sweet charming, hypnotizing, some posts compare them to a vampire and their alluring charms and how they take hostages. My view is that they take willing hostages. You are willing to put up with the BS.
Doesn't sound like you are very happy now are you? The thing is you can't help an alcoholic, they have to do stop drinking by/for themselves. You will never be worry free dating an active alcoholic.
He won't see the severity of his drinking if he has a loving GF who is always there, makes excuses for him and tiptoes around him. I know this is hard to hear but you are enabling him. You aren't helping right now because you have gotten wrapped up in his drinking problem.
Who cares what others think, you know the truth. It's not just fun and games, he has a serious problem.
Many in the forums mention the 3 Cs. You didn't cause it, you can't control it and you can't cure it. All you can do is work on yourself. I would recommend going to a local al-anon meeting.
You only get one life, do your research and do what's best for you. You are also important, don't forget that.