The inner corners of my eyes are sore and weeping?

Conjunctivitis: You might have conjunctivitis, which can be highly infectious so you should get it checked out. http://www.ncbi.nlm.nih.gov/pubmedhealth/pmh0002005/ you might also have an allergy.

Tearing, eyelid: Eyelid irritation in the corners can have many causes and is best sorted out by an eye examination. Excessive tearing may cause sore eyelids, especially when accompanied by rubbing. If there is a bump in the corner, there may be a blocked tear drainage duct. See an ophthalmologist.