A corneal abrasion is exactly what it says it is. It occurs when something (a finger nail, a pencil, a stick) mechanically scratches the cornea and removes some of the epithelium that covers the surface. It is not an infection. A corneal ulcer is an isolated (can be large or small though) area of inflammation related to an infection of the cornea by a pathogen. The most common cause of a corneal ulcer is bacteria, although ulcers can occur associated with other pathogens such a viruses or fungi. These are active infections and should be treated agressively by either antibiotics, antivirals, or antifungals. As to your last question it depends upon what type eye drop you are talking about. It is possible that you may be allergic to an ingredient in the eye drop. Only way to know for sure what is happening is to go in and let a doc take a look.