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Hello and thank you for using this site to help you. They do make a cortisone cream just for dogs and you can find it in any pet store. This should help the itching until you can see her vet.
Usually icthing and rash under the arms are from an allergy to food, so make sure to mention to your vet that you have changed the food.
I am sorry for the delay, my computer crashed. Here is more information on the Hydrocortisone use for dogs. It would be a good idea to invest in a cone so he cannot lick it.