As I have written before, there are many natural options (cleansing & moisturizing) that will bring good results in healing the skin of eczema breakout. Neem oil is one of the many natural products that are beneficial to skin rehydration and healing. Your current skin care regimen seems to be working towards the process of skin healing. Likewise, oatmeal baths aren't the only options for bathing. For us, it was the Burt's Bees buttermilk product line. If you've found a store that provides good organic/natural products for bathing and moisturizing, I am sure that there are other options for bathing that are equally beneficial for the skin, apart from the oatmeal bath. Vitamin E bath oil, aloe & calendula are some of the other options to consider. Personally, I think that you have already found a good alternative for bathing with your introduction of the neem bath product. Basically, I think that you've addressed the external sufficiently. At least give it another week to determine its effectiveness.
Remember that I have said there are three parts to address when healing the skin of eczema (internal, external, and foreign). I'm not clear if you've determined what your child's particular allergen/irritant is. This is very important to discover; in order that the good work you're doing to help the skin heal is not being made counter-productive due to the fact that the allergen/irritant is still in the child's environment.
If I've given you the impression that all doctors are bad, then I've done a poor job in articulating my point. Several of my family members are in the medical field as well (for generations now). In every profession, there are both good and bad representatives of the professions. In America, there are a lot of politics involved in the medical profession. Doctors (too often) are caught in the middle between the pharmaceutical companies lobbying and patient care. Eczema and Acne are big business for these companies; thus the longterm approach to patient care (symptom suppression as opposed to skin healing) is promoted and encouraged. This has been the case for my mother's persistent suffering for almost 40 years now. For me to deny this truth, I would be chosing to spare the feelings of the medical community at the expense of continued patient suffering. When my nieces were born, I couldn't remain quiet; nor could I stand back and watch them suffer in the same way that my mother has suffered all these years. I don't hate doctors or medicine. I don't think that all doctors are bad; however I do know that all doctors aren't good. We learned not to blindly trust the physicians and to weigh information given to us with common sense wisdom. In other words, we took from them what was good and threw away what was bad. In order to fix what is wrong in the medical profession, you have to be able to acknowledge that it is not perfect or without flaws. Your husband happens to be one of the good doctors. He understands the origin of modern medicine from its natural predecessors. I consider you to be blessed to be married to what I consider to be a precious gem - a good doctor.