Perhaps a biopsy of your facial skin would yield more information than any more lip biopsies. SjS is not all that associated with super tight, red, dry, cracked skin. Most people with SjS have dry eyes and dry mouth and often + blood work, at least the ANA, and sometimes the SSA and SSB. Depending on your doctors and other symptoms, a lip biopsy may or may not carry much weight. ALL meds have side effects and they all have risk.
Scleroderma is more associated with tight problematic skin, but, that is also associated with +ANA, sometimes, but not always, Scl-70 antibodies. There are many forms of Scleroderma. Usually dry painful skin is not the only issue.
Usually with the autoimmune issues, there is some pattern that gives the doctor a clue as to which one it is....and that clue is symptoms and blood work.
I agree with Irish, that the lip biopsy is not a for sure thing. I am an RN as well. I can't recommend self medicating.
Your diagnosis could be something totally different....it is important to get the diagnosis correct...not necessarily rapidly.
Since you are in so much discomfort, I would see a dermatologist....if your skin is your biggest issue right now and a derm could potentially assit you to get an accurate diagnosis, whatever it may be.