Is it necessary for someone who feels urine or madhy (prostatic fluid) has exited to check and look to confirm if anything has come out or not, especially if this feeling is recurrent and sometimes they find something and sometimes they do not?

If your feeling of something exiting is mere doubt, then you are not required to investigate. Rather, build upon the original principle, which is that nothing exited, because certainty is not dispelled by doubt. The Prophet, peace and blessings be upon him, said to someone who imagined finding something during prayer: "He should not leave until he hears a sound or perceives an odor." This is further emphasized if you are prone to frequent doubts.