Any suggestions as to how to cope with the warm, dry air in my house?

It’s cold. The air in the house is stuck with no place to go. It’s getting kind of stuffy and dry. On top of that, we have special heating that makes the house stay around 80* in the winter, no matter what. (Yeah, we wear shorts and t-shirts all year long.) Because of this huge difference in temperature – 0* outside and 80* inside – any moisture inside the house condenses on the windows and then drips down onto the sills. They get moldy if we’re not careful, so we have to make the house as dry as possible.

I have problems with the dry air every winter. The skin around my nails dries out and peels, which is really painful. I get nose bleeds. My allergies actually act up, too! I almost always have a stuffed up nose. My hair dries out and gets all frizzy. It’s all around a bad time for me.

We air out the house as much as possible.
I drink tons of water (a gallon or more every day).
I use tons of lotion and chapstick.

Do you have any suggestions of supplements to try, foods to eat, something to put in my room, or anything else? I’m getting kind of desperate.