Get rid of the carpet! If you can't afford hardwood, go with linoleum if you have to. Over the years, the ointment and lotion residue will build up in the carpet and even if someone with ichthyosis isn't living in the house, the buildup of crud that gets trapped by the carpet and carpet pad is gross anyway. It's also sooo much easier to keep the floors clean without carpet.
Since we had the carpet taken out of the apartment and linoleum put in my sinus headaches are much more minor, I don't get anymore migraines, and I haven't had a single skin infection. Most allergy docs recommend their patients remove their carpets anyway.
Kirby vacuums used to be quite good (I don't know if they still are), but when it comes to skin peeling from ichthyosis I don't think there's a vacuum on the market that can do a good enough job. My dad used to do carpet cleaning and repair and he says carpets are one of the dirtiest nastiest things people have in their houses.
If you really must have rugs, at least get area or throw rugs so you can lift them up and take them out and clean them and get the floor underneath clean as well.
I am female, and was born in 1972 with Lamellar Ichthyosis.