One of our cats has had chronic licking/bald patch/hairball/vomit issues for most of her life. The vet has prescribed various treatments over the years: new diet, prednisone, shots, anti-anxiety medication, creams, etc. Nothing really worked. Expensive allergy test revealed nothing. Eventually I got tired of seeing my cat being treated as a guinea pig on my dime so I just stopped taking her to the vet. If not better she's doing no worse than when she was being treated. But, yeah, take your cat to the vet. Hopefully it's a treatable condition.