Your forgiving him has nothing to do with whether you want to live with him while he is actively drinking.
Alcoholism is progressive and it gets worse if untreated. You have a right not to be subject to random "tantrums" even if it's just the two of you, and you certainly don't need to be belittled and put down in front of others.
Sounds like you made the right decision for you to get some peace in your life. The two alcoholics I was married to were nice people, too, when they weren't drinking. I eventually had to get space from both of them. One got well, and hasn't had a drink in thirty years (we divorced for other reasons). The other is still drinking, so far as I know. The point is that I didn't CAUSE the drinking, I couldn't CONTROL it, and I couldn't CURE it.
Whether your "fiance" (are you still engaged?) gets well or not is up to him. If you see him on an occasional basis, he may be able to hold it together while he is with you, but still be someone you don't want to spend time with, much of the time. You might want to tell him (but this is up to you) that you don't want to see him until he's gone six months without a drink. Or you may just choose to move on with your life, and if he gets well, you can revisit the relationship.
At least this way, you have some breathing room to decide what you want for yourself. I would suggest some Al-Anon meetings. They can be very helpful in sorting out your thoughts about where this might be headed and what you want for yourself.