Over the last few weeks, my right arm, from just above the shoulder blade down to the wrist has been in pain. Most of the time, such as now, it's a 2 or 3. When I wake up, it's 4 or 5. If I try to reach behind me, the pain increases - I stop it around 7. When I cough the pain level clears 7, maybe 8.

I am a 46 year old male, in moderately good shape (cardio hikes 1 hour each 4-6 times per week with light strength training.)

Is this pain something that likely requires a doctor visit, or will resting the arm allow it to heal on its own? What are the likely causes & cures?

Thank you.

It's not your left, the side of the heart.
Sounds like a pinched nerve on the shoulder on down the arm, very common.
It hurts when you cough just because you are using a lot of muscles to cough.
So... moist heat on the shoulder, stand in shower, lie in tub, put warm towel around your neck, rotate your neck and shoulder gently while sitting doing nothing, take Tylenol (pain) and ibuprofin (inflammation).
I personally would see a chiropractor before I would see a MD, if it comes to that.

And if you spend a lot of time in front of a computer using your right arm and hand, that could be your actual culprit. If your desk top is too high, your shoulder hunches up.