Burning sensation in center of back between shoulder blades, & upper abdomen, comes and goes. Can this be pinched nerve, acid reflux or something more?

Nonspecific. There are a number of possibilities, including soft tissue inflammation, muscle sprain/strain, facet mediated pain, rib fracture, herniated disc, intrathoracic pathology, etc, as well as pinched nerve and acid reflux as you have stated. If your symptoms do not improve with time and conservative treatment (i.e. Anti-inflammatory meds), do see a physician.