I shorted a circuit, reset a breaker, now much of the house electricity only works if I turn on a wall AC unit
Possibly the main breaker partially (only one pole) tripped in addition to the individual circuit.  Since it is presumably an older breaker, this is not out of the realm of possibility.  A newish breaker would have definitely completely tripped.

Start by switching off the main breaker and then turning it back on while carefully noticing if the spring action of both poles are resisting turn on.  (Don't worry if you cannot tell.)

If all circuits come on then you are good, though scheduling replacement of the main breaker should go on the todo list.

Otherwise, it is possible that the panel's bus bars need tightening or other maintenance.  Remove the panel cover and have a look for anything amiss:  wires dangling, soot, melted metal, melted plastic, discolored metal bus bars, discolored lug screws, etc.



Once I mis-wired a replacement electric stove top switch so that when a certain pair of switches were both on, it placed a complete short across the 240 supply.  It tripped both the range breaker and the main.  The range breaker was melted internally.