My MRI said I have a "intrtasubstance tear of the glenoid labrum". Celebrex (celecoxib) did nothing for me. Do I need surgery?

Diagnosis? Be careful about assuming that the MRI reading is the same as a diagnosis. If you are having shoulder pain that has not responded to conservative treatment, get a second opinion with a shoulder specialist to establish a diagnosis and cause of your shoulder pain before making the decision for any surgery.
Possibly. If conservative treatment doesn't help, arthroscopic surgery would be helpful. This surgery can be done with a few small incisions as an outpatient with good results.
Maybe. Mri is a non invasive diagnostic test. Consider mr arthrogram to see if tear might be more extensive than seem at regular mri.