You can read here about using aspirin in dogs
http://lowchensaustralia.com/health/aspirin.htm
But you may find glucosamine chondroitin will also be a help - you can use about 1000-2000 mg per day split over two doses.
If she isn't on flea prevention that might resolve the biting issue. Good info on skin allergies here
http://www.lbah.com/allergy.htm
Benadryl can be used in a dose of 1mg per pound of dog on up to 2mg per pound every 8-12 hours but it may make the dog sleepy.
My fear with the dog with diarrhea is that this could be a sign of a closed pyometra.
As the other dog isn't ill with the same thing that limits hope that this is from an infection with coccidia or giardia or other parasites or a bacterial infection. Usually dogs that live closely together end up with the same 'bugs'. But it might be that.
You can see if some fiber will help her control the diarrhea - canned pumpkin, cooked winter squash, sweet potato, oatmeal all can work well to absorbe excess fluids.
You can see if bland food will help her too. Boil chicken or hamburger and drain off the fat then mix remaining broth and meat with plain white rice for bland food.
I do think you need to figure out some way to get transport to a vet for the younger dog.
Hope this helps you!
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