There is a superficial layer of tissue called conjunctiva overlying the sclera. A swab could be used by an ophthalmologist at the slit lamp to determine if the lesion is at the layer of the conjunctiva (will move with the swab) or sclera (nonmobile). The lesion could be resected if it is at the level of the conjunctiva although if it is at the sclera, may be more challenging to cover.
The spot is on the screla.
Can The Spot Be Removed or Covered?
I would go see an oculoplastics specialist since a pigmented lesion that is changing over time is suspicious for melanoma.