My Hands are cracking very easy developing what looks like burns

@antman69 Welcome to Mayo Connect, where patients and caregivers meet to help one another through life's ups and downs.
Did you know that one of the most common places to develop skin cancer and pre-cancerous lesions is on the backs of your hands?
Have you had your primary care provider take a look at your hands?
Another possibility - some medications make the skin very thin and vulnerable - have you started any new ones lately?

Have you seen a dermatologist? You could have a form of eczema; there are a dozen different types of eczema some with specific known causes and some forms with unknown causes. Go to dermnetnz.org which is an amazing site filled with photos of different skin diseases. Try to find a photo that looks like what your rash looks like.
You could even be allergic to the cream you apply, best to simply moisturize with plain Vaseline until tested for the allergic form, Allergic Contact Dermatitis, ACD. I never had infected rashes, so no need for an anti-biotic topical like Bacitracin. Never wash dishes without a barrier glove, vinyl and plastic usually allergy free, but do not use rubber, nylon, neoprene or other materials with blended ingredients. Dish soap, Dawn for example triggered the beginning of my ACD issues because of the preservative in it. Then washing with a glove that had rubber in it exacerbated it. The 5 Day Extended Patch Test identified over a dozen of my contact allergen's for me to avoid. That said, normally ACD manifests as hundred's of little papuales to form a rash. Dysidrotic Eczema, DE on the other hand manifests as a flat red patch on very dry skin. DE attracts the hands and may also attack the feet. The website I directed you to will have these photos.
I never had skin issues, not even acne, until middle age when I developed 3 different forms of eczema (an auto immune disease) which I now have totally controlled. There is no cure, avoidance of food and contacts can help some forms and steroid's can initially provide relief but best to avoid because of side effects with chronic use.
You didn't mention itching or pain. That is also a helpful diagnostic tool.

Good information above.
Soaps are bad. If it only on your hands then it is something you are using.
Dawn soap is bad for me. I wear gloves when I clean
There are some great mild soaps that clean very well. Don’t listen to the ads on TV that are pushing any kind of soaps.
Wish you the best.