Shoulder impingement. You need to get out ahead of this ASAP. Here’s the deal:
You need to ditch any bench pressing short term. Long term, you’ll likely need to relearn your technique. Do you bench press like a bodybuilder with flared elbows so you get more “chest pump”? Are your Dumbell presses also “wide?” That shit has got to go.
First of all, ditch any of the dumbell presses and learn the standing overhead (barbell) press with your forearms entirely vertical and inside of your shoulder frame. It’s probably going to feel very “narrow” and the position is going to be more out in front of you. At the top of the press, perform a full “shrug” extending maximum possible range of motion. This will strengthen your rotator cuffs, but this is a slow process. Over time, you can100% correct impingement with pressing and until you feel healed back up, this will be your only pressing movement. No dips, no dumbells, no KBs, no accessories. I’d drop the archery practice for a couple of weeks and then Come back with a 40# bow, super conscious of your technique. After strengthening your overhead press considerably, this should not be enough stress on your shoulder to matter.
Eventually, you will be able to bench press again, but its going to be with your forearms vertical and your elbows tucked tight to your body. All of the Bro, “chest pump” days are done. If you do resume dumbells, it will be the same technique: vertical forearms, 0 elbow flare and arms tucked tight to your body. The more perpendicular the elbow angle, the more damage you will do to rotator cuff.