As from your history you are complaining a white growth nearing the black part of the eye.
The black part which you are referring is cornea
and probably the growth which is approaching the cornea is pterygium
. There is no medical treatment for pterygium and medical treatment is limited to treat some complications of pterygium like inflammed pterygium.
The treatment for pterygium is mainly by surgical treatment
. The commonly done surgery is pterygium excision with conjunctival graft.
kindly do consult your eye doctor for examination and treatment accordingly.