Are you actively pulling the shoulder blade into your body for an organized shoulder position?
You may not have optimal hand placement.
Have you looked at your pressing mechanics?
Pressing Mechanics and The Knee Pushup Up Disaster/Froning and Bailey Edition
Episode 236: Overhead Wrist Dysfunction

Do you know someone who has a slingshot you can try?
I’ve used it with several people to correct/better understand hand placement and positioning.
Movement Transfer Exercise: The Pushup & The Slingshot
Are you missing range in your shoulder?
Episode 158: Normal Shoulder Have FULL Range
Episode 34: Bridal MWod: Bride/Operator Shoulders; IR Rotation/Scap Gliding