Your shoulders are rounded so it is a situation that needs attention. Everyone is different in what their body can/will tolerate with deviations in technique.
Are you warming up enough before horizontal pressing?
Where this is a trouble area it may require a longer warm up/warm ups sets.
Are you cooling down following following the session?
What are your sliding surfaces in these areas like?
Pain can come from adhesions and or tacked down skin getting pulled in opposite directions.
Do you know of anyone in your area who does soft tissue work?