Oven broiler has stopped working, but broiler element seems fine
You have lost 1 leg of the 240v supply. 
If you disconnected 1 of the leads there would be 0 or 120 in both places. 
If both legs of the 240 are switched by a relay one of the contact sets have failed. Or a bad connection. Since bake works I would be tracing the circuit to the control  relay. The element shorting may have damaged the relay and now it has failed would be my guess. 

If you have access to the board you may find the right one by cycling and finding the relay that clicks , if you can find a schematic the broil relay will probably be labeled. These Relays are usually under ~15.00 and will usually have 6 connections to the pc board 2 for control 2 hot in and 2 hot out, there may be an extra set that is not used but these cost more so it will probably be just 6. 

Most of the time they are encased in black or white plastic once you verify that is the problem unsoldering and replacing the relay will make it just like new.