If it hurts, I recommend backing off the full bench presses. You are only going to continue to increase the inflammation at the AC joint if you try to "push through the pain". I'd stick to board presses, floor presses, or other variations that limit the amount of shoulder extension, which is going to be what irritates the AC joint the most. Try some push up variations too to see if they are more shoulder friendly as well.
Also, make sure you are getting plenty of scapular stabilizer work in - rhomboids, lower traps, serratus, etc. If the scapula is not sitting properly, the AC joint won't be either. Check for hypertonic/overactive upper traps, scalenes, and SCM as well, as these can lead to an elevated scapula and/or clavicle.