You’re not telling the age of your baby ?
Causes and common triggers include of eczema are: irritants – such as soaps and detergents, including shampoo, washing-up liquid and bubble bath. environmental factors or allergens – such as cold and dry weather, dampness, and more specific things such as house dust mites, pet fur, pollen, moulds and diet.
These are all facets you can look at. I would step by step eliminate causes and keep a diary of it’s effects

You need to get to the cause of the eczema! Cortisone prescription medication only heals the skin, it does not fix the issue.

Could be from a number of things:
Washing detergent
Soap
Allergic reactions to milk/formula/food including fruit!
Over heating
The list is endless! Eczema generally shows up in babies in high heat zones like where you have described but will spread once Bub works out it’s nice to scratch!

Get into it early!!!

My son gets it on his face and cheeks, the doctor said to use QV wash and to moisturize with plain sorbolene cream, he said if it gets worse he can prescribe steriod cream but it hasn’t come to that yet

I have found a wonderful natural product called COCONUT BODY MILK and it is purchased in some stores (you can check out where on their website) or buy online. It has no nasties and has many testimonials on working on this kind of thing. http://www.ecotan.com.au/shop/uncategorized/organic-coconut-body-milk/

If you are in a humid climate it may be caused by constant moisture, perspiring etc. It may be worth speaking to a pharmacist, and state that you want something as natural as possible. It depends whether the skin of it is dry or moist. Don’t dress her in synthetic materials at all.
Wool isn’t the only fibre that can cause irritation. Some can’t wear polyester, nylon or viscose at all. Try to use cotton only.

there are a number of foods too which are believed to trigger eczema. may be worth looking into.

Use a baby friendly skin cleanser, moisturize as naturally as possible, keep away from wool clothing and dont let him soak in tub.. That works for our baby

I had three children with eczema, one that still has flare ups. I could not find a trigger for my first two children, however my third child seemed to flare up with strawberries in particular but also with fruits, tomatoes etc which led me to think perhaps salicylates could be the cause – never confirmed. Tried many creams, medications etc including Elidel which seemed to work but has now been linked to cancer. Was not happy with steroid creams for a number of reasons. I now only use gaiya ointment – natural made from native bees wax. For my children it was better than hydrocortisone creams or anything else, so good in fact I now help my friend make it. it is a small scale production to say the least due to the limited amount of wax native bees produce but it is the best thing I have personally come across for eczema. https://www.facebook.com/pages/Gaiya-Ointment/536514513148497 Other great advice I have received is to moisturise loads (and I mean loads), avoid soaps, fragrances etc and take heart, children do seem to grow out of it.