Thank you for the additional information.
There are a couple of possibilities that can cause an inability to move the arm.
It is certainly possible that the injury also damaged the nerve to the arm or the area around the nerve, but this would require a wound that is deeper than the subcutaneous tissue. Since the inability to move the arm was not present immediately, it is more likely that the injury was of the tissue around the nerve and inflammation and swelling of the tissue created pressure on the nerve days later. If the piece of glass had directly cut a nerve there would typically be immediate loss of function, so that the inability to move the arm would be noticed the day of the injury.
It is also possible that there could be some secondary musculoskeletal inflammation that can occur following any trauma, even if there had not been a cut of the skin or deeper tissue.
Although it would require a proper evaluation to determine the specific cause, there are a couple home interventions
that can be tried to help with musculoskeletal inflammation, and if these interventions help, then no further evaluation or treatment is necessary. These interventions include taking an over the counter anti-inflammatory medicine, such as ibuprofen or naproxen, and the application of ice to the area of injury, which can help reduce swelling.
If the ability to use the arm returns with the use of anti-inflammatory medicine and ice, then it is less concerning. However, if the inability to use the arms persists, then it would be appropriate to be seen again.
If I can provide any clarification, please let me know.