I am Dr. Will and I will try and help.
You say these look like warts. When you scrape them off, is there any fluid in them? Do they bleed. Would you say they look like pimples? are they black or white or pink?
I will watch for your reply.
To be this numerous, I am suspicious of a dry staphylococcus dermatitis. Staph can get into the sebaceous glands and hair follicle and cause swelling like you are describing.
I would use a good medicated shampoo or even just use chlorhexidine soap. Scrub the skin thoroughly and then rinse with an apple cider vinegar solution of 2 tablespoons of vinegar to a gallon jug of water. Let her dry. Repeat weekly.
This should reduce the problem.
If this makes a difference, skin antibiotics such as simplicef would be very helpful. You might speak to vet about prescribing some.
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Thank you and best wishes, = Dr Will