Sclera discoloration can have a number of different causes, some benign and some that are dangerous to a person's health. Most over-the-counter eye drops treat reddened sclera, usually through a preparation that decreases the size of surface blood vessels. Brown spots on sclera may not respond to that kind of treatment, and the underlying disease may require medical intervention, so it is advisable to seek professional medical assistance rather than attempting to self-diagnose or treat.
Not all brown discoloration is caused by the same thing, so it is important to first diagnose the most probable source in order to decide if treatment is required. In general, most brown spots are benign in nature and either are present from birth (like a freckle on the eye) or are a normal development with age. Some eye discoloration can be caused by medications such as chlorpromazine, or by ingestion of gold. Others can be due to scleral melanocytosis, which is benign as well and is more common in Asian populations. Dark-skinned populations can have "muddy" brown sclera as a normal variant from their increased number of melanocytes. Any brown spot that appears to be growing or changing shape, however, should be evaluated by an ophthalmologist to ensure it is not cancerous.
Regardless of cause, brown spots can only be removed through surgical procedures and must be done by a licensed and qualified medical provider. If the spots are of cosmetic concern, it is unlikely that insurance companies will pay for the surgery to remove them. If the spots are cancerous, the ophthalmologist will determine the appropriate treatment and possibly refer the individual to an oncologist for any follow-up chemotherapy that may be required. All surgical procedures must be done by a licensed eye doctor and must never be undertaken by a lay-person.
The two surgical options are to excise the affected area of sclera only, or to remove the conjunctival layer of the eye (called a "conjuctivectomy") and allow it to regenerate without the brown pigmented area. If surgery is required, the decision about which method to use is up to the ophthalmologist and will vary between individual cases.