Based on your apparent pain threshold, it will be a couple of days before you want to bite down on anything. The pain drinking etc. really should be noticeably improved in 24 hours. This is mostly from the cutting done. Yes your teeth were probably impacted, coming in at an angle and so pressing on an adjacent tooth or the rear of the jaw. They even sometimes have to chip away a (small piece) of the jaw. It is going to hurt. Your jaws should hurt tonight if that is of any consolation.
Non-narcotic pain relief is usually not very helpful the first day or two. Some doctors do not like to give pain medication. I would just choose a new dentist. Ask around. During the initial visit give them your story and ask their philosophy on relieving pain. If you don’t agree move on. Most dentists will at least give you a dozen Tylenol w/codeine after surgery.
Percocet is a schedule II drug. Some dentists/doctors choose not to be able to dispense these types of drugs. Most states have more stringent regulations on prescribing these drugs and many states actually charge more to obtain the ability to write these prescriptions, substantially more. Those who choose not to prescribe these generally have an associate that can prescribe if really necessary. Some states might even require this. Or he could have prescribed them for you and just took them himself.