Thanks for using the forum. I am happy to address your questions, and my answer will be based on the information you provided here. Please make sure you recognize that this forum is for educational purposes only, and it does not substitute for a formal office visit with your doctor.
Without the ability to examine you and obtain a history, I can not tell you what the exact cause of your symptoms is. However I will try to provide you with some useful information.
Postoperative swelling and pain can persist after neck surgery for several weeks. However, it sounds like your surgeons do not think that your swelling is related to the surgery. It is difficult to understand exactly where the location of your swelling is in relation to your surgery, but generally speaking, causes of neck swelling can include swollen lymph nodes (such as occurs as a reaction to a surgery or infection), thyroid enlargement, or other masses. One option if your symptoms do not improve is evaluation by an ENT, to evaluate for neck problems. Sometimes, a CT scan of the neck provides more information than an MRI of the neck area in regards to the soft tissues in the neck, the lymph nodes etc. Another possibility is that your pain is muscular, due to muscle spasm, what is termed myofascial pain, which could be treated with anti-inflammatories and pain medications.
Continued followup with your physicians is recommended.
Thank you for this opportunity to answer your questions, I hope you find the information I have provided useful, good luck.