I suggest you see a dermatologist, you say they are getting bigger and awful looking. If you keep your baby in long coat not a grooming problum, my passed girl was kept in a puppy cut, there was a wart that I had not seen and was shaved off by the groomer, I won't go into detail of what it looked like and the vet bill I had to pay.
Bumps, lumps, any kind of a skin growth can be an issue if your baby sports a puppy cut.
Is it you or your vet that does not want it surgically removed.
These growths could be tumors, maybe a 2nd opinion by another vet is in order. If my vet told me they were "old age spots" but they are growing I would getting a 2nd opinion or, off to a dermatologist. JMO