Thanks for the input, everyone.
Rachylou, are you saying that the redness I see is just from having a different spectrum of light, as opposed to my skin actually being red? I suppose that could be possible for the flushed skin, but my eyes felt irritated (I had some eye pain) as well as appearing to be bloodshot, so there was something definitely going on with my eyes. I will also say that I have a brain injury and therefore have some neurologic issues...so maybe I'm more sensitive to the wavelength of light of the CFLs.
I am not particularly fond of LEDs. I have an LED desk lamp that is OK but kind of irritating (very cool light, like at Walmart). I have also read that LEDs can interfere with your sleep cycle more than other types of lights, and I already have sleep issues, so I'm kind of hesitant to try them. Has anyone tried halogen bulbs? I think that's about my only other choice, besides a kerosene lamp. Ha.
Lara, I have read that some places recommend staying a few feet away from the bulbs, because they emit UV rays that can be damaging. So that might explain your experience. In my apartment, the light above the stove as well as the lights above the bathroom vanity would have been closer to me than just a few feet, so maybe those were causing most of my problem. I knew about CFLs not being able to be disposed of in the trash, but I am upset that the apartment complex did not tell us that. I assume everyone in the building thinks they can be treated like regular light bulbs. You are also supposed to be very careful about how you clean them up when they break, and that was never mentioned either. Grr.
DoubleH, yes, I suspect that there is something about the wavelength that my brain doesn't like, and it is manifesting this way. As I mentioned, I have a brain injury, so all bets are off as to what the CFL wavelength is doing to me. My doctor suspects that I have a low tolerance for EMFs, so maybe that is part of the issue here too.
I did switch out the bathroom vanity bulbs and the bulb above the sink and will avoid using the overhead lighting for a few days to see if that helps. I do have regular lamps that still have the incandescent bulbs, so I won't be completely without light in the living room. It's too bad, because I really liked the light from the bulbs better than that from my incandescents. It wasn't like Walmart at all—it was warm. Sigh.