I suspect when you pick him up, you are touching a spot that may be painful or overly sensitive. I would start getting him used to the carrier by leaving it out and open, perhaps with a favorite blanket or toy inside. Encourage him to go in the carrier by placing treats that he will do anything for. Once he feels comfortable going in the carrier, you should have no problem getting him in there when it's time to go to the vet. Please let the vet know when you make the appointment and again before he examines your cat that he sometimes bites so that your vet will be prepared for any situation.
