when you hurt a muscle, there may b localised swelling. If you think of the back muscles as a jacket that you wear, and underneath that all your nerves and blood vessles run. Tightness in the back at shoulder blade height could constrict or apply pressure to the nerves across your shoulder, into arms hands etc. I think blood vessles run across the front but i can't remember without looking it up? Doctor will most likely prescribe ibuprofen 400mg (like 2x the ones you get from the super market). You can take these yourself, best bet is to speak to a chiropracter or massage therapist (try to avoid ones who practice in their underwear, They look nice, but their prices are steep and they tend not to know too much about anatomy!)
Mention to them that you have an active problem as some may not want to work on you until it has settled down. Keep moving the affected arm round and keep moving your neck. In fact, any movement that hurts, do it! The worst thing you can do with non traumatic back pain is sit/lie still as the muscles will then seize up, making recovery take even longer.
If I was allowed to prescribe, I'd write you out a script for ibuprofen, Good rum, Ice cream and some qulaity old war films. That and a week off work to recover.
Good luck!