I'm a physiotherapist
it sounds like you have what we call impingment syndrome. The muscles stabilizing the shoulder blade during movement are weaker than the prime movers (eg pecs, delts during bench). There are also likely muscle imbalances in the area (tight pec minor, lats and teres major). Weak muscles would be lower and mid traps, SERRATUS ANTERIOR, and infraspinatus.
I would recommend a visit to a GOOD physiotherapist....preferable one in a sport clinic so they understand you want to train.
Otherwise .....stretch the pec minor in a doorway....arms at 90 degress and elbows bent to 90....forearms flush to door frame...
3 X 30 sec
strengthen serratus by lying on your back ....two dumbells in the locked out bench position now move them controlled uup and down vertically without bending the elbows(all mov't at scapula)
3 X 30 reps
3rd do shoulder press without weight (initially) standing with back against wall with forarms flush. as you move the arms up try to pull the shoulders down....thus increasing the contraction of the lower traps. YOU SHOUULD NOT FEEL PAIN OR YOUR UPPER TRAPS WORKING!!!
3 X 10 reps
All ex's 3 X day
remember your not weak ...just not recruiting the muscles properly. This program takes dedication.
Stop using barbell for a while so you can use a natural range for YOU. And incline instead of flats.
Good luck ....
email me with any other Questions.
HM