Large Red Veins in Sclera?

Steroid eyedrops raise the risk of cataracts, glaucoma, and infection (particularly herpes).  These should not be used without careful monitoring by an ophthalmologist.

Some large episcleral vessels remain dilated indefinitely (like a balloon after being deflated).  While this can be managed surgically (such as cautery), usually that is overkill.  Don't use Visine on more than a very occasional basis -- rebound redness is common.

Engorged vessels will often regress with treatment of dry eyes, although it may take some time.  This may or may not require steroid drops depending on the severity.  Your own ophthalmologist should evaluate your eyes before you decide on a specific course of treatment.