Sounds like you may have a secondary bacterial infection if so many things are causing your lips to burn. It sounds like yeast because my lips used to burn a lot too and when I got a culture test done years ago it turned up to be yeast.
My current culture tests have turned up to be negative so, I'm over my bacterial infection. I am just focusing on the inflammation now.
I lightly and gently peel my lips after I brush my teeth because that is the time in which the buildup is the weakest. I will not force it off but lightly move my lips over one another so that my lips allow the buildup to come off. Sometimes the buildup falls off by itself. This is ideal to do when using a steroid cream because the cream will have to work less to penetrate the skin of the lips & thus assist with the source of the problem.
I drink alcohol very rarely. But I do like rum, whiskey, & vodka. However, I drink very, very rarely & I don't drink to get hammered either. I try to drink water as much as I can. Eight glasses a day is the recommended amount and more than that during the summer.
You need to find a good barrier cream. Have you tried the vitamin E gelcaps?