What is the physicalogical process and part of the body that a male feels "pressure" and needs to "release" sexually?

It is called the arousal system. I would google it to get details as is complex. Another option is to go to uptodate.com and get a 1 month subscription and read all about it. Then if a problem discuss with your Drs.

Almost all normal male 'feel' the urge for sex and 'pressure' and 'release as part of being male due to a complex interplay of hormones and nerve stimuli and expressed in the brain centers as desire for it and its expression thru sensory and motor nerves