I’m not using aloe any longer. I found that using it at night would cause a premature exfoliation of the lip skin the next morning, impeding the healing process. The dead skin actually seems to help heal when the lips are moist with water and sealed with balm. When the skin comes off, it comes off :)
For a reference, my lips were almost identical in terms of severity to lipshitz and dhammaboy on the peeling lips wiki webpage.