Back problems for years. it's now radiating down the arm. doc wants to do trigger point injections, should i do it?

Trigger points: Can't hurt... Worst case, you get an anti-inflammatory in your system (depomedrol (methylprednisolone) in injection). Better result if diagnosis more confirmed. Trigger point not likely to explain arm pain. That sounds more like a pinched nerve. Regardless, if not worsening, any treatment (pt, shots, anti-inflammatories) ok as first try.

Back and arm pain: How far down the arm is the pain radiating? What is the quality of the pain? These answers would be helpful to evaluate causes and direct treatment.

Yes: Successful injections can provide an "honeymoon" period pain relief so physical therapy can be tried. Is probably underlying shoulder disorder. Look at "normal" posture of your head & neck. Are you tilted or is one shoulder lower? Chronic localized muscle spasm can lead to development of trigger points. Regular walking has helped many who have neck muscle imbalance from one side to the other.