Any rebound redness due to use of a mild vasoconstrictor like Visine should clear in a week or so. Because there are a legion of causes of red eyes I cannot offer an opinion that would be helpful. Even non-ocular problems like hyperthyroidism can cause red eyes. I would suggest a consultation with an ophthalmologist (Eye MD) that specializes in 'external eye disease' (usually a cornea specialist). Most medical schools will have such an individual in their department of ophthalmology.
Good luck
JCH MD