I finally made it to the doctor yesterday, who told me that I have what's known as a "marginal corneal ulcer." This link clearly and concisely talks about it. The doctor gave me two different medications to take. He indicated that I secondarily also have "blepharitis", which has exacerbated the problem, though I seem to have a very mild form of it.
Interestingly, the doctor said that I have a high pain tolerance as most people, when afflicted with these ailments, are typically in to see the doctor immediately and are largely incapacitated. When I told my wife this, she nearly snorted in derision. She knows me much better -- I'm a total wimp when it comes to pain, who will take a sick day if I feel even slightly sniffly.
After taking the medication, my eye is now looking quite normal with the redness nearly all gone. I am supposed to take these two eye-drop medicines four times a day, which is something I really don't like doing. My eye still feels a little "warm", and I have a little bit of light sensitivity, but I'm in pretty good shape now. Unfortunately, the doctor wants to see me in a week (instead of saying, "Come back if you have any further troubles!"), which means I may be in for a long treatment.