If the runway was changed whilst you were on final why did you re-position? Runway changes aren't instant - if you're on final then you're on final, end of story. Think to yourself - if an airfield changes while you're on final - is there actually going to be anyone final to the cross runway? No.
Dependent on where other aircraft were in the circuit there is a point where you decide who's going to be for the old runway, who's going to be for the new runway, and anyone who taxi's from that point of decision (not before, obviously) goes for the new one.
If you were doing circuits - never a problem. Touch and go on the old runway and then join straight downwind for the new (if it's a Left Hand Circuit with the directions you say) or extend slightly upwind to sort yourself out, turn right to re-position crosswind if 11 was a Right Hand Circuit.
Having you go-around whilst on final because a runway change is poorly managed is extremely poor practice.