I am sorry your baby has this trouble.
It sounds like miliary dermatitis.
Your vet is correct to limit steroids because they can cause diabetes and renal failure in cats.
Yes it is safe to use plain neosporin three times a day.
Fortunately cats do not get as many skin conditions as dogs so they are much easier to diagnose and treat. They can be allergic reactions, fungus or infection.
Here is the most common with photos:
Stud tail:and feline acne
Ringworm can be recurrent and is treated with a topical fungicide or a vaccine shot.
miliary dermatitis can come from a food allergy or the bite of even ONE flea.This is treated with one cortesone shot or neosporen it is safe it he licks a bit.
Granuloma is also usually allergic in nature and can be treated cortesone or antibiotics or both.
There is also alopecia which is usually symmetrical and can be self inflicted:
A staph infection is also a possibility and can recur at times when the immune system is weakened temporarily.
Please look at the photos and let me know which best relates to your cats issues and I will be happy to discuss this further with you.
Warmest best wishes,