Radial Head Fracture: The patient's history of carrying a heavy bag and hearing a "pop" followed by pain and weakness in the forearm, particularly with rotation, suggests a fracture. The radial head is a common site for fractures, especially in older adults, and the symptoms align with this diagnosis.

Interosseous Ligament Injury or Forearm Compartment Syndrome: The swelling or muscle bulge in the proximal forearm could indicate an injury to the interosseous ligament or the onset of compartment syndrome, both of which could result from the trauma described.
Biceps or Triceps Tendon Strain: Although the bicep looks normal, strains in the biceps or triceps tendons could cause pain and weakness, especially with flexion and rotation movements.
Radial Nerve Injury: Given the symptoms of weakness with external and internal rotation and flexion, an injury to the radial nerve, which controls these movements, is a plausible diagnosis.

Acute Forearm Compartment Syndrome: This is a medical emergency that requires prompt intervention. If not addressed, it can lead to permanent nerve and muscle damage.
Vascular Injury: Any significant trauma to the forearm could potentially damage the arteries, leading to ischemia or other severe complications.

Olecranon Bursitis: Although less likely given the mechanism of injury and the specific location of pain and swelling, olecranon bursitis could cause swelling and pain in the elbow area, potentially radiating to the forearm.
Ganglion Cyst: A ganglion cyst could cause a bulge and potentially some discomfort, but it would be less likely to cause acute weakness and pain following a traumatic event.