I can't tolerate most detergents either, and fabric softeners not only give me skin reactions, but breathing trouble as well. I've been successfully using Ecover and Biokleer detergents, available in the nutrition sections of some stores like Fred Meyer.
And I generally add one cup of white vinegar to the rinse cycle to help remove all residue – it also helps deodorize and soften clothes.
For the itch/rash itself, you might wish to try another product that I've found to be wonderful; Florasone cream, also sold in nutrition centers. It has a bit of an herbal smell, but really does a number on itching, and I've read a number of reviews by people who said it helped heal terrible rashes. I would try just a small area to start, and avoid any open/weepy areas because it can have a slight sting.
Oatmeal in the bath can be soothing. Test it first: Make a slurry in a cup of hot water and apply it to just one patch of skin, and give it 24 hours to make sure she won't react to that as well.
Ask your doctor about the benadryl before giving it. You'll need to know a safe dose for your sweetie. I'd also ask if cortisone cream would be a reasonable thing to try (though Florasone cream may be even more healing).
I've also known adults (including me) and children to get amazing relief from a good homeopath. The first visit includes an extensive interview and can cost a couple of hundred dollars (be sure to ask when you call), but follow-up visits are cheaper than an M.D.'s office, and the remedies are affordable.
Be aware that just because this was diagnosed as contact dermatitis, that may not be the only problem. There could be other allergens or irritants at work, too. Bath soaps, shampoos, moisturizers, and many common foods, including milk, eggs, many grains and acidic fruits. Keep looking for answers if clean clothes don't significantly improve your poor little's condition. Good luck!