JKZ, ask your vet to do blood tests, don't delay. I can't explain the fur-pulling but six months ago my 10-year-old cat was throwing up all the time, lost a third of his body weight, and a blood test proved that he has chronic kidney disease, which is very common in older cats. It gets to quite a bad stage before symptoms show and the biggest symptom is sickness because so much bile builds up in the stomach, the poor thing was desperate for food but kept chucking it back up undigested. The vet kept him in over the weekend to rehydrate him, and he is now on a daily tablet (the cat, not the vet) and loves them, and is back to his old bouncy loony self. If your vet won't do that, then change your vet - your cat needs urgent help.