You ARE doing the right thing. For one thing, you've probably already taken on some of their traits, and for another, it's just time. You are NOT your parents' keeper!!! You have your OWN life to live -- your life does NOT revolve around making sure your mother doesn't fall, or that they don't fight!
I know you love your parents, but being around two probable alcoholics is really frustrating. They say and do things they wouldn't normally say or do when they're sober. They can sometimes act like children. Their fights are disturbing and maddening. They can sometimes be just plain disgusting! Who wants to be around people like that?
You are like I was. My mother never taught me anything either, i.e. cooking. She didn't want me in the kitchen. So when I got married, I was the worlds' worst cook!
But you learn quickly when you HAVE to.
A good cookbook is your bible. lol Cleaning is no big deal, and washing clothes-- just read the instructions on the bottle/box of detergent! LOL And as long as you pay your bills on time, you'll be fine.
You might do well to attend some Al-Anon meetings too -- these are for people who have family/friends who are alcoholics. I'm sure these will help you cope. Go 2-3 times and see what you think. You can take what you like and leave the rest.
I wish you the very best. I hope you find a place soon -- I think you're right about moving out. Take care and God bless. Hugs, Lee