If you haven't talked to your primary care doctor
about this yet, that would be the first step. You need a doctor to take a look at your eyes and help figure out whether this redness and itchiness is coming from.
By far the most common cause of red and itchy eyes is allergic conjunctivitis. The type of allergic conjunctivitis that you are most likely familiar with is the kind caused by seasonal allergies, which it sounds like you do not have. However, there are other types allergies which can cause redness and itching of the eyes. These include various "indoor" allergies, such as allergies to mold or mites. These symptoms can occur year round.
Another potential cause would be blepharitis, which is an inflammation of the edges of the eyelids. Blepharitis is often caused by chronic irritation from eye makeup or other chemicals. However, it can also sometimes be caused by a viral or bacterial infection.
Your doctor will be able to examine you and confirm which diagnosis--either one of these two, or another condition-- you have. Based on the diagnosis, they will be able to recommend appropriate treatment, which might include anti allergy eyedrops or pills, or antibiotics in the case of an infection.