What is the best treatment for burn marks caused by a home remedy for acne?

I fully agree that the burnt marks are likely to be due to irritation from the home remedy. Very often, certain products or home remedies can cause excessive irritation of the skin and this can lead to redness, inflammation and sometimes crusting of the skin, which often resolves with post inflammatory hyperpigmention. It is best to stop the treatment to prevent things from getting worse.

It is unusual for the acne lesion to turn into a mole. This needs to examined before we can advice further.

It is best to see a dermatologist/ doctor to help manage your skin issues.

Please do not continue with home remedies for your acne, as a lot of such remedies are completely unsubstantiated, and may often cause more harm than benefits.

The burn marks you’ve experienced are probably due to the acidic nature of vinegar, possibly having been left on your skin for too long. This will recover with time, and leave behind some post inflammatory hyperpigmentation (PIH).

PIH is probably also what you described to be the mole-like spots left behind by acne.

Please consult a dermatologist or doctor with an interest in skin, who will be able to help manage both your burn marks and acne.