A beer cock is essentially what we call a ‘tap’. In Dunmore’s time, they were gravitic; the keg or barrel had to be above the cock. You can see old beer cocks in numerous beer museums and/or on a tour of an old-time brewery. I know they’re part of the tour at the Urquell brewery in Plzen and the Carlsburg brewery also have them, I think.
A “beer cock” sounds like a personal problem. Call a doctor.