Unfortunately there's a huge variance in PT quality and skill levels, so just because 6 weeks of PT doesn't produce results doesn't necessarily mean that a different approach to PT wouldn't be better than surgery. Seriously, have you tried visiting a McGill Method Master Clinician? I would certainly try that before letting a surgeon cut on me. Watch the video I linked above and see if it might be relevant.

What sort of injections are you referring to? Corticosteroid injections can sometimes be helpful in the short term but clinical practice guidelines discourage prolonged use due to the risk of bone damage and other severe side effects. So insurers aren't necessarily wrong to deny payment for those.