Why don't fish get hurt with so many sharp fish bones? And why don't fish feel pain when they swim? Don't those sharp fish bones stick into the flesh while swimming?
Connective tissues prevent fish from being hurt by its bones. They surround the sharp bones so that the bones do not hurt its organs/flesh.
However Of course the bones can hurt the fish, but the situation is quite imaginable.
If a fish is smashed or gets too much force, its connective tissues cannot protect its organs much(like our clothes cannot protect us from bullets, or our broken bones penetrating our organs when we encounter a serious car accident despite our connective tissues covering the bones - the bones just damage our connective tissues and organs, and so on...) and its organs get hurt.
Your worry can happen in human case too (but much weaker version), we can think of our hip bones sometimes pressing our flesh between the bones and the chair we are on.