Eye hemorrhage. If your are describing a redness confined to a segment of the white of one eye this may be a subconjunctival hemorrhage. These can be caused by trauma, coughing, straining, weight lifting but are most often occur with no noticeable cause. High BP and anticoagulant meds can potentiate these. These are often benign and require no treatment. Slight tenderness is common but pain/visual loss are not.
Dryness. The vast majority of conjunctival hemorrhages are caused by dry eyes which can be helped with artificial tears. Sometimes, the bleeding can be worsened by use of anticoagulants such as Coumadin (warfarin) or plavix. Other causes include uncontrolled blood pressure and bleeding disorders. If you have headaches or other symptoms, please see your ophthalmologist right away.