Local Reaction to Vaccine: This is the most likely diagnosis given the temporal relationship between the vaccine administration and the onset of pain, without any history of injury. Local reactions such as pain, redness, and swelling are common side effects of vaccinations.

Bursitis or Tendinitis: These conditions could be related to the injection itself, causing inflammation of the bursae or tendons in the shoulder. The lack of injury history still makes this a plausible option due to the potential for the vaccine injection to cause mechanical irritation.
Referred Pain: Sometimes, pain can be referred from other areas, but given the direct correlation with the vaccine site, this seems less likely unless there's an underlying condition causing referred pain to the shoulder.

Septic Arthritis or Osteomyelitis: Although rare, these conditions are serious and could potentially occur if the vaccine injection site became infected. Given the time frame and the absence of systemic symptoms, this is less likely but should not be missed due to the potential for severe consequences.
Neurological Complications: Rare neurological complications such as brachial neuritis could potentially occur post-vaccination. This condition involves inflammation of the nerves and could cause significant pain and neurological deficits.

Complex Regional Pain Syndrome (CRPS): A rare condition characterized by chronic pain, inflammation, and hypersensitivity after an injury or trauma, which in this case could theoretically be the vaccine injection.
Vaccine-Induced Immune-Mediated Diseases: Certain vaccines can rarely induce immune-mediated diseases such as Guillain-Barré Syndrome, though this is more commonly associated with systemic symptoms rather than localized pain.
Shoulder Impingement Syndrome: While not directly related to the vaccine, this could be a coincidental condition that presents around the same time as the vaccine was given, especially if there was pre-existing shoulder instability or overuse.