This cold weather and the furnace running in your house a lot probably are contributing to the skin condition. A good shampoo & rinse can help.
I just posted this in another thread

-- but hope this can help you too.
Most of these will require a waiting time -where you shampoo & then wait 3-10 minutes before rinsing, then the conditioner will probably be the same way. So you want to make sure you have the bathing area really warm before you start the process. Also, rinsing is the most important part of a bath. Let me make a couple of suggestions for shampoo & a rinse.
This one was recommended by my holistic vet - this is the website for the shampoo, Phytoclens Herbal Shampoo - you can buy from them.
natural herbal treatment - tomer laboratories - natural quality herbal remedies
I would definitely find a good shampoo -- this one contains:
PHYTOCLENS Herbal Shampoo
Phytoclens Himalayan Cedar Shampoo contains the natural essential oils of Himalayan cedarwood (Cedrus deodara) and Eucalyptus leaf oil (Eucalyptus globulus). Phytoclens use in a regular regimen promotes healthy skin and coat.
This is what I found about those ingredients
oils of Himalayan cedarwood
Cedarwood Himalayan Essential Oil, Cedarus Deodora
Eucalyptus leaf oil
Eucalyptus Globulus Essential Oil, Eucalyptus globulus
Or this is also a good choice for a shampoo & a rinse that will help dry skin & at an Excellent price!
HyLyt Shampoo (8 oz) and this rinse Relief Creme Rinse - 8 oz
At the very least find a really good oatmeal shampoo. Numerous brands have good oatmeal shampoos
I'm also wondering what type of food you are feeding. There could be an allergy issue. Your baby may also benefit from Missing Link being added to the food or at least of salmon oil