New, or adult-onset growths on the sclera is highly unusual. The most common scenario is that of growth in the overlying layers, i.e. the conjunctiva or subtenons tissue (which lie above the sclera).
Conjunctival growths may be benign or malignant. The most common of which are reactive immune-system related growths called follicles or papillae.
Malignant or pre-malignant lesions including carcinoma in situ(CIS) should also be excluded, as well as pigmented lesions.
Subtenons tissue may proliferate and cause granulomas, or undergo metaplasia, causing pinguecula, or pterygium which is related to sun exposure. The range of differentials is wide.
You should consult your attending Ophthalmologist for an accurate assessment and discussion of your management options.