Just as a little test, try some seated dumbbell presses. Check out the position of your wrists, elbows and shoulders. Does it look the same on both sides? As you press, do the dumbbells move in the same path? If your shoulders are slumped, they may not be slumped to the same degree. If you're really crooked, you may be better off using dumbbells for awhile, as you improve your shoulders. If you're pretty square, you should be OK to press, as you work on your back and shoulders.
When you rack your bench presses, check out the position of the barbell. Is it centered on the hooks, or way off to one side? Does the bar helicopter or kayak on you?
As far as getting your shoulders in position, I love the "Deisel Crew Feel Better Right Now Shoulder Exercise Combo" as a warm up. Those moves were new to me, so they felt really good.
Band-Pull aparts and band dislocates are effective and easy.
Bottoms up kettlebell presses are good. You really have to "pack your shoulder" to stay tight and control the kettlebell.
Also, blast straps, or TRX handles are good. You can do combo moves, sorta crossing rows and external rotations and face pulls, all at once.
Try some stuff out, see what you like. Fighting had posture is going to be part of your life now. Find a couple moves you like, and use them as a warm up before upper body days. Pick 2 or 3 easy ones, like push-up plus and band pull aparts, and do 2-3 Sets, two or three times a day, outside the gym. You'll be countering the effects of your job, almost like rehab. But moving your upper body around daily will also help you recover faster from upper body workouts. Doing extra work outs for your lagging body parts will build you up, and improve your lifts. Its win/win/win.