This is what I use every week on MY 1 year old, dry baby girl. Take a small glass bowl or whatever bowl you want to use. Use one heaping (maybe more if you're baby is big) tablespoon mayonaise (not miracle whip and not the fat free or reduced fat variety) 2 or 3 tablespoon olive oil (I use extra virgin because I have it in the house), 1 Egg. First fluff the egg with a fork, add the oil and whip some more. Last, fold the mayo into the mixture and you have the perfect, cheap, all natural hair mask! If the smell bothers you much then you can add 2 drops of essential oil. Place doggie in the tub and rub the mask on like you would shampoo your baby, careful around the little face and eyes. Be generous around the belly and leg area. Leave on for up to 15 minutes but for a least 5 min.! Rinse the goo off your baby with your shower sprayer and wash baby with your usual shampoo 2X. Let the last rinse be a little cool to seal the hair follicles. Skip the conditioner, you won't need it! It's done wonders for my girl's limp coat and dry skin!
You can also make your own detangler with colloidal oats and aloe that won't dry the skin! When you have a dog that has dry and sensitive skin, it's best to use products that are chemical free and as natural as possible! Also, don't use water that's too hot, it further dries out the skin! You can also try Wild Sockeye Salmon Oil, it has the most Omega 3 of all fish oils! I get mine from Vitalchoice dot com, 500 mg is plenty! Prick one open and drizzle over your baby's food once a day. Hope your baby feels better soon! Dry skin ain't no fun!