Are there any over-the-counter products that get rid of pinkeye?

Possibly. Pinkeye is common language for conjunctivitis. Commonly, this is due to allergies or infection by viruses or bacteria. Over the counter drops may help allergic conjunctivitis. Normally, one would find other allergy symptoms such as itchy eyes or sneezing. Bacterial conjunctivitis is usually treated with prescription antibiotic drops. Spread of infections can be reduced by hand washing.
PInkeye. Most pinkeye is viral in origin for a normal healthy adult. It typically is caused by a type of cold virus and may last for up to 4 weeks. Supportive care includes cold compresses and artificial tears, such as theratears, genteal, or systane. Avoid contact with others, and avoid sharing towels or pillows, since this is highly contagious. If your eye does not improve in 2-4 weeks, seek help.