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Excessive grooming around the tail and back usually is a result of flea allergies. I know it isn't really spring where you are...but fleas can live in the house. They can also start this as a psychogenic licking cycle where they do it as a compulsive behavior.
I recommend getting an injection of a cortizone from your vet...it decreases the lick cycle. The vet should be able to tell from looking if it appears more "allergy" vs. compulsive issues. The injection lasts about 4 weeks...if flea then get a good topical prevention.
The hairballs are secondary to the grooming. Any over the counter hairball medicine 2-3x a day for the first 3 days and then weekly is suggested.