A red line - I suppose its a vein; If its just that red line/vein without any irritation, infection, watering - It could be normal. The reason for such thick vein could be long term exposure to dust, wind, sunlight, excessive near work, less sleep, high system use, strain, a/c rooms ... Resolving it back to normal might take months provided the lifestyle is changed; But to halt the process of congestion(increased blood vessels) ; its good to instil tear drops in eye along with omega 3 fatty acids orally. hope this helps :) *Kindly do not ask for prescriptions as we are not supposed to write medications online as per MCI guidelines.