Temporomandibular Joint (TMJ) Disorder: This is the most likely diagnosis given the presentation of bilateral jaw pain. TMJ disorders can cause pain in the jaw, face, and surrounding areas, and are not necessarily exacerbated by chewing. The chronic nature of the pain over two months also supports this diagnosis.

Bruxism: Grinding or clenching of the teeth can lead to jaw pain, and the fact that the pain does not worsen with chewing does not rule out this condition, as bruxism often occurs at night.
Dental Problems: Issues such as abscesses, impacted teeth, or periodontal disease can cause jaw pain. Although the pain does not worsen with chewing, these conditions should still be considered.
Sinusitis: Inflammation of the sinuses can refer pain to the jaw area, and chronic sinusitis could explain the duration of the symptoms.

Giant Cell Arteritis: Although less common, this condition can cause jaw pain, especially when chewing (jaw claudication), but it's essential to consider due to its potential for serious complications, including vision loss.
Multiple Myeloma or Other Cancers: Metastatic disease to the jaw or primary jaw tumors are rare but critical to diagnose early due to their significant impact on prognosis and treatment.
Trigeminal Neuralgia: A condition characterized by intense pain in the face, which could be mistaken for jaw pain. It's crucial to identify due to its distinct treatment options.

Eagle Syndrome: An elongated styloid process or calcified stylohyoid ligament can cause jaw and facial pain. This condition is rare but should be considered if other diagnoses are ruled out.
Sjögren's Syndrome: An autoimmune disorder that can cause dry mouth and lead to dental issues, potentially resulting in jaw pain. It's less common but important to diagnose due to its systemic implications.
Osteonecrosis of the Jaw: A rare condition often associated with bisphosphonate use or other medications, which can cause jaw pain and is essential to recognize due to its challenging treatment.