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. http://www.youtube.com/watch?v=cz-kdc7bhww&list=uu15uuhuqiy9zdpywwxf31jg&index=1.
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.