Entire area of lips, but primarily near edges, are red, swollen, and chapped. does not look like a cold sore as it's all over, what else could it be?

Hard to know: .. without examining them. Could be dryness, however, living in Denver I suspect you are accustomed to using balms for dry lips. One thought is that you have a sensitivity to some additive in a lip balm or cosmetic. Try using Aquaphor for a few days to see if there is improvement and, of course, maintain good hydration. Good luck!