It's a little difficult to tell from your question what exactly is going on since there are many parts of the eye that could be affected, and the best thing would be to see your doctor
to have them take a look at your eye and advise you.
If the part of your eye that is normally white is red, this could be because of inflammation either of the conjunctiva (called conjunctivitis) or of the layer underneath (called episcleritis). Conjunctivitis can be caused by a viral or bacterial infection, or by allergies or irritation from contact lenses. Herpes infection of the eye can sometimes look similar to conjunctivitis but can cause serious complications if untreated. A small foreign body lodged in the eye can also cause irritation and redness and would be important to remove. Episcleritis looks similar to conjunctivitis but is usually more localized and is not bad in and of itself, but can be caused by autoimmune diseases and is therefore important to diagnose. Sometimes dry eyes can cause mild discomfort and redness and can also be caused by autoimmune diseases. If a vessel has ruptured in your outer eye, this can also cause redness, though would usually go away within a couple weeks. Other more dangerous causes of a red eye, which would usually be accompanied by visual changes, include keratitis and uveitis. Finally, inflammation of the eyelid, called blepharitis or a nodule on the eyelid called a chalazion can also produce redness.
Because there is such a large list of possible causes of a red eye, and given that your eye hasn't gotten better over three weeks, I'd strongly recommend you visit your doctor to have them take a look. Even if the eye itself isn't in danger, some of the syndromes can be caused by an autoimmune disease and it is important to make that diagnosis. I would start by seeing your primary care doctor
, who can decide if you should see an ophthalmologist
and if necessary make a referral.