Those are hives. Its a reaction to something. The thing is with all the changes in food, and detergent - there is no way to determine the cause. Give her some Benadryl, and just watch to make sure there are no breathing problems. It could take a few days for the hives to go down. If you start to notice any problems breathing, get her to the vet immediately as they will need to inject her with something stronger. I would go back to basics with everything. Go back to old detergent. Go bland with her diet for at least a week, after the week of bland - start mixing in the new kibble day by day.
The bath & benadryl should help alot.