My Flight was canceled after I checked my bag ,baggage claim worker told me they would put it on the next flight but I booked with a different airline because All flights were booked. Now I’m in Austin and my bag is still in LAX has not been scanned

It's simple process but the convenience it causes is a whole other story but simply call the airline you orginally booked from have give them you're luggage number so that they can locate it then the will send it directly to you via private local carrier deliver it to you wherever you are staying

Did you or airline book the trip to Austin? Was your final destination Austin when the booking was made on the others airline they could have put a request to retag your luggage. I know that luggage doesn't need to follow passenger. Put a claim to deliver your luggage to where you will be at Austin