Hello and Welcome to ‘Ask A Doctor’ service.
I have reviewed your query and here is my advice.
Shoulder presses can certainly cause strain if the neck and other muscles as one has to strain a lot and can cause pains and spasms.
When you have doing the exercises, it is possible that the muscles of the neck got an
injury causing pain while swallowing.
There is a possibility of spasm of the muscles around the throat that is pharynx causing a feeling of swallowing a ball.
Hence I would advise you the following:
Consult your Doctor for clinical evaluation and examination.
Ask for a reference for an ENT Surgeon so that an ENT
endoscopy to know the exact cause.
Get an
MRI of the neck.
All these will give a proper diagnosis thus giving you a proper plan of management.
Do not wait for self healing as delayed treatment can cause complications like
fibrosis.
If the reports are normal then an anti-inflammatory medications will help to have cure.
Hope I have answered your query.
Let me know if I can assist you further.