May not be tooth. There are other possibilities other than a piece of tooth in this area. It may be a bony protuberance or a bone spicule. Have it evaluated to determine exactly what is causing the problem and to determine your options for treatment.
Residual? Have you been seen by a dentist? Wisdom teeth are frequently oddly shaped and may be fractured to begin with. I would check to see if you do not have a residual piece of the tooth.
An x-ray. Will determine and identify specifically what the structure you have in the area. Please see your dentist asap esp. If it is irritating your cheek or your tongue.
No. Removal of wisdom teeth should have no negative effects on chewing or swallowing. If you are having problems swallowing, make an appointment for an examination with an ENT specialist.
Post op evaluation. You need to return to the dentist who removed your wisdom tooth to evaluate exactly what is causing you the pain. It may or may not be related to the surgery. There are many possibilities and only a dentist who can actually examine you can determine the cause of your pain.
Not uncommon. Unfortunately most wisdom teeth surgery is accompanied by some degree of pain up to 3 weeks. For the pain management, you can take an Rx medication by your oral surgeon and alternate with NSAIDs OTC. If concerned, visit your surgeon for post-op appointment.
Not normal. Not normal. Return to extracting dentist for exam.
It depends. Speaking regarding wisdom teeth removal, there is no doubt that today that it can be done very confortablely with excellent anesthesia and IV sedation that you wake up and everything is done without you remembering a thing. Premedication with anti infamatory and anti swelling perscriptions can make even your experience afterwards very comfortable.