Jamie's skin is super dry (and I call her my little alligator sometimes hehe) and both of my kids have had eczema. Gavin has outgrown it, thankfully. I never have gotten to feel truly baby soft skin with Jamie, though. Winter has really made her skin worse. We live in a 90-year-old house and the air is very dry. I'm surprised I haven't had a nosebleed yet this year, but I suppose its not as bad as the house we lived in last winter.
I would suggest a bath every other day instead of every day like you said. I know that Jamie's skin is always pretty red after any bath. If it doesn't get better with Aquaphor, try Cetaphil or the wal-mart equivalent brand. Get the tub of cream, not the lotion. The lotion is pretty good, but the cream is better. It has been so good for Gavin's and Jamie's skin. We also only use All free and clear on Jamie's clothes and most of the time on all of our clothes, and only fabric softener on my husband's clothes and only the sensitive stuff. I have asthma and allergies year round, so I found that I can't go back to nice smelling detergents and fabric softener either