Hello, 
I have studied your case.
According to your history and complains yes such kind of pain can due to compression of nerve and muscle 
sprain due to boxing .
Another differential can be 
rotator cuff injury which may need MRI for confirmation.
Medication like methylcobalamine with 
muscle relaxant and 
analgesic will reduce pain, you can take them consulting your treating doctor.
You may consult physiotherapist for further guidance. He may start TENS ,or 
ultrasound which is helpful in your case.
You may need to take rest for early healing.
Some exercises which can be done after pain has reduced include- gradual neck rotation, touching your ears to shoulder, shoulder shrugging exercises. 
Also check your vit B12 and vit D3 in your blood.
Hope this answers your query. If you have additional questions or follow up queries then please do not hesitate in writing to us. I will be happy to answer your queries. 
Wishing you good health.
Take care
Regards 
Dr Vaibhav