Cervical Radiculopathy: This condition, often resulting from a herniated disk or bone spur in the cervical spine, can cause pain that radiates down the arm, including the shoulder and forearm, matching the described symptoms. The burning pain and deep ache are consistent with nerve root irritation.

Thoracic Outlet Syndrome (TOS): TOS involves compression of the nerves and/or blood vessels that pass into the thoracic outlet (the space between your collarbone and first rib). Symptoms can include pain in the shoulders and neck, and can radiate down the arm, which aligns with the symptoms described.
Subacromial Bursitis or Rotator Cuff Tendinitis: These conditions can cause pain in the shoulder that may radiate down the arm, especially with movements. However, the specific location under the clavicle and the deep ache between the bones of the forearm might be less typical.
Referred Pain from the Gallbladder or Liver: Gallbladder disease (like cholecystitis) or liver issues can sometimes refer pain to the right shoulder due to shared nerve roots. This could potentially explain the shoulder pain but might be less likely to cause forearm symptoms directly.

Myocardial Infarction (Heart Attack): Although less common, myocardial infarctions can present with atypical symptoms, including pain in the arm, neck, or jaw. Given the potential severity, it's crucial to consider this diagnosis, especially if accompanied by other symptoms like chest pain, shortness of breath, or nausea.
Pulmonary Embolism: Similar to myocardial infarction, a pulmonary embolism can present with sudden onset of chest pain and, in some cases, referred pain to the shoulder or arm, necessitating immediate medical attention.

Pancoast Tumor: A rare type of lung cancer located at the top of the lung, which can cause shoulder pain due to local invasion of the brachial plexus or ribs. This would be an uncommon cause of the described symptoms but is important to consider due to its serious nature.
Brachial Plexitis (Neuralgic Amyotrophy): An inflammatory condition affecting the brachial plexus, which can cause severe pain in the shoulder and arm, often followed by weakness. It's a rare condition but should be considered in the differential diagnosis due to its distinct presentation.