Redness in the upper part of one eye is commonly due to mild causes like irritation, dryness, allergy, or a small burst blood vessel (subconjunctival haemorrhage), and it can also occur with conditions like conjunctivitis or eyelid inflammation. In most cases it improves with simple care such as avoiding eye rubbing, using lubricating eye drops, keeping the eye clean, and protecting it from dust or smoke, but you should see an eye doctor if the redness lasts more than a few days, is associated with pain, discharge, swelling, vision changes, or follows an injury, as you may need specific treatment like anti-allergy or antibiotic drops. Meanwhile, avoid self-medicating with over-the-counter steroid drops unless prescribed, as they can worsen certain conditions.