Are there non-surgical methods to remove a brown spot on the eye sclera?

Making any diagnosis from a photo is often challenging. Photos sometimes do not fully represent all the features of the lesion in question. An important question to consider is when the lesson was first noticed? Very commonly, long-standing pigmentation on the conjunctiva as seen on the photo can simply be a nevus, or “mole”. Spots that require closer medical attention are those that are of recent onset and progress rapidly (few weeks and months) as this may indicate the presence of a tumour instead. Quite frequently, there is no need to remove the nevus, as it is often harmless.

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.