The the brownish stain in your eye could a melanosis
which can be in the sclera or conjunctiva
. This is due to certain cellular changes and will not go with any kind of eye drops. You should be aware that usually these are benign conditions but rarely if they change in colour, shape or size then you should seek opinion as these changes point towards abnormal growth and a biopsy
is recommended to rule out any malignant change. It is always a good idea to photograph it for comparison purpose.