Hi,
According to your question, the white layer at the edge (that is where the black portion of the eye meets the white portion) could be a benign condition called Pinguecula (sometimes can be because a Pterygium). Sometimes this condition can give irritation to the eyes.
Next Steps
You should start on some lubricating drops like Refresh tears eye dropd, 2 drops 4 times/day both eyes.
Health Tips
In case the pain/irritation or redness increases, i suggest you see an Ophthalmologist