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It seems to be partial second degree burns. Keeping a dressing to cover it is optional. If you have acess to a "sterile dressing pad set". A topical antibiotic called Silver Sulfadizine can be used (available as OTC only in some locations.) It is placed after the application of topical antibiotic and consists of a first layer of nonadherent gauze (eg, Adaptic®) placed over the burn, a second layer of fluffed dry gauze, and an outer layer of an elastic gauze roll (eg, Kerlix®).
But if there is not much exposure of the burned area to outside and there is less chance to get in dirty (while work etc) then you can just leave it open without any dressing or ointment and keep a close watch.
Hope this helps
Feel free to ask follwoups
Thank you