The average passenger doesn't often get to experience a hold awaiting weather to stabilize. Sounds like some kind of storm front was passing causing the wind to start changing while you were on the approach. The flight crew would have waited for the new wind direction to become established, and, if there was any other traffic, wait in turn for the next approach.
So it would have felt bumpier than most are accustomed to. No big deal, though.
A go-around is an aborted landing. A missed approach is a go around from an instrument approach, with a particular path and climb gradient to be followed. Don't let the terminologies confound you. It all pretty much amounts to the same thing; the nose goes up, the power goes on, you climb, you don't land off that approach.