There are many reasons for dog's to develop red, itchy skin. Anything from a thyroid condition to a flea allergy causing flea dermatitis (even one flea bite can cause a world of problems to dogs that are sensitive to them) to allergies whether chemical or food related to yeast infections. If this is ongoing, it is best to have your vet take a look and do a skin scraping to start ruling out parasites like mange or issues like yeast. Yeast is likely as per the odor you are smelling. Read more about yeast below and treatments.
Click here: Yeast Infection of the Skin
Click here: Benzoyl Peroxide Shampoos (to treat yeast infection)
Look into the type of dog food you are feeding...if it lists corn as the first ingredient, consider a food switch to a holistic diet like Eagle Pack Duck and Oatmeal. (please do remember it can take up to 6 weeks to notice improvement after a food change). Your vet may do some bloodwork including a T-4 thyroid test.
Now to help give your baby some relief at this point...a cool oatmeal bath will help to settle the inflammed skin. Providing your dog is not on any other medications, you can give him/her plain Benadryl 1-2mg per pound of body weight every 8 hours. This will take away the itch and also help with the redness.
I wish you and your baby all the luck and hope he/she gets some much needed relief soon. :)