What is the average time for scars to heal after electrocautery?

Since the mole on your upper lip is raised, I would recommend a shave excision.  This should remove the mole so that it is not protruding anymore, but it is possible that there still could be some pigment remaining.  If the pigment still bothers you, then you would need to have it...

All moles should be excised and set for pathological examination. After freezing the mole, the freezing would destroy and no proper diagnosis is possible.See a plastic surgeon for excision of the area and hopefully there is enough pigment left that can be examined and hope for the best

Anytime a mole is growing or changing, I suggest it should be evaluated in person by a dermatologist. The ABCDEs need to be used when examining your skin, and in this case, 2 of the 5 are happening, so you need to make an appointment to have it checked properly. "This answer has been solicited...