Hi..
Welcome to HEALTHCARE MAGIC..
I have gone through your query and can understand your concerns..
As per your complain it seems that due to burning of the skin there has been inflammation and the dark circle seems to be due to post inflammatory
hyperpigmentation that occurs due to excessive production of melanin in that area as a protective phenomena leading to darkening of skin or dark spots..
I would suggest you to firstly start doing cool compresses over it..
You can apply creams containing Kojic acid,
glycolic acid and arbutin over it..
You can also apply Vitamin E and C containing creams..
Wash your face with
Salicylic acid and Glycolic acid containing facewash..
If the skin in the area has healed then you can also start scrubbing your face twice a week using a mild scrub..
Limit sun exposure as it can further cause increased pigmentation..
You can also
consult a Dermatologist and get evaluated and he can advise you ointments containing Steroids to be used under caution as they can heave side effects..
Treatments like
Microdermabrasion can also be advised..
Hope this information helps..
Thanks and regards.
Dr.Honey Nandwani Arora.