Do people with corneal abrasions have a lot of pain?

Yes: They are exquisitely painful.

Yes: The cornea has a very high concentration of pain sensing fibers, tucked just below the single layer of skin. An abrasion will expose a large number of pain fibers and cause significant discomfort. Luckily, the cornea is also the fastest healing body part. A large abrasion can completely heal within a matter of a few days, rather than a few weeks for other body parts.