Is true that barbell bench presses damage the anterior capsule?
I have anterior shoulder pain. This pain can to be
tendonitis?How to cure such pain?Celebrex?

Bad technique, bad recovery, bad warmup…can be dangerous.
Barbell bench press is only an exercise…
Some muscles are out of balance, ART, or another soft tissue management technique can help you!
Ice, natural NSAID (ginger o arnica), basic trigger point work, light EMS are great as self treatment.