Your problem sounds very similiar to what I once had... unexplainable pain just under my left shoulder blade. It seemed dull at times, sharp at other times... it felt like the pain area was the size of a quarter and deep under the skin, prob underneath the shoulder blade.
It was ultimately traced to a pinched nerve near my spine.
I went to back doctors or this matter. This old doctor, thought this is a highly unpredictable case, his best guess... it will go away linearly over time... gradually decreasing over a few months. He was right in my case. In the meantime, I was experiencing extreme pain - scale of 5-6 on the 1-10 pain scale. So painful, it was a constant reminder... of pain.
Hot pads, cold pads... should be applied to the spine area, not the actual area of pain. Be nice to your back and remember, nothing comes on or goes away overnight. It's very hard to tell if you doing the right (or wrong) thing because changes occur so slowly. You may have to sleep in the "correct" position for a week before you notice any improvement. If you sleep in the "incorrect" position, it may be a few days before the pain increases. So... experiement with different sleeping positions.
My pain went away over 4-5 months... I was on powerfull narcotic pain killers for a couple of months until the pain was more toleratable. Then I was completely gone. BUT, it came back again. I was on painkillers again. Then this time it slowly went away - for good.
In the five years since, it never bothered me again. I can carry heavy backpacks, hike, climb all I want now.
Every individual is different... my best guess, you might have it for a few months.