It's strange that dumbells would be better for you, but it could be the difference in hand positions with the pushups. Are you doing the dbs with a neutral grip?
Try doing the pushups with small dbs in your hands, with the same wrist orientation as when you do the db presses. I only say small dbs so you are closer to the ground. The actual weight doesn't matter.
Pushups are important because of the scapular freedom that they allow. Try and see if you can make them happen without pain.
However, if they still hurt, don't do them and try to figure out what's what.