There are different types of shoulder pain/injury. Hunching over also (for a lack of proper terminology) narrows the groove in which the bicep tendon sits in which can cause inflammation.

Do you do a proper warm up? You should be increasing your heart rate (temporarily) and core body temp prior to lifting, for shoulder days I also do rotator cuff/shoulder warm ups (banded internal/external rotations, face pulls, pull aparts, forward and lateral raises), and then pyramid sets up to your working sets.

Make sure when you're benching you're getting good scapula retraction and depression (shoulder blades pinched and down) with some arch in your back, and tuck your elbows (don't bench with flared elbows).

These are all important to keep your shoulders happy, if you suspect an injury talk to a doc.