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Post waxing burns are quite common especially in sensitive areas like the face..after a hot wax..but such burns are usually superficial in nature and heal up without much scarring or pigmentation.
I would advise you to keep the area clean and dry,,use an antiseptic solution or lukewarm water to clean the area twice a day
Apply an antibiotic cream like mupirocin
gel...as this will decrease the chances of superadded infection as any kind of infection over the affected area will lead to increased chances of scarring and pigmentation.
Also use a sunscreen regularly before going out in the sun....
Take oral antihistamines like levocetrizine once a day to reduce the redness
You can additionally take oral vitamin C
supplementation in order to speed up the healing process.
The burn will heal in a span of 5-7 days if proper care is taken,,,after that, if any pigmentation persists, then you can apply a mild lightening agent containing kojic acid
over the lesion till the skin colour returns back to normal
Hope it helps
Dr Geetika Paul