The departure GA wanted you onboard so the aircraft could depart. Standing at the gate giving the GA a hard time is not merely not productive, but counter-productive. You should count yourself very lucky that the GA didn't simply close the flight and leave you standing there.

Sorry for your condition, but there is nothing more which could have been done given that you apparently did not make prior arrangements for an escort between gates. It is also not feasible to make announcements at a major airport, you don't say where you were, but it has at least 2 terminals, about minor delays at a gate in another terminal. Personnel also don't know that the aircraft will be held, so all they can do is push you to get where you are going as fast as you can.