The neutral grip (palms facing one another) is the best grip to use if overhead pressing exercises are bothering your shoulders.
With the elbows pointed slightly forward instead of straight out to the sides, press the dumbbells using a neutral grip. Bring the dumbbells close together at the top without touching them.
The first rule of fixing your bench press is admitting your bench sucks. The second rule is that you must read this article and learn about the set-up, grip, ascent, and descent.