I fly out of a controlled airfield and we mix with 737s on the ILS all the time. It happens regularly that either ATC instructs us to orbit, or that we are called "number 2 to the 737 on 4 miles final" and we ask ATC for an orbit. But all that happens on downwind. Having to break off an approach while on final either suggests very poor planning from ATC, or extreme dallying on the pilots part, causing a ruin of ATCs plans.
In this case I would probably call ATC afterwards, tell them I was a bit shaken by the whole situation, and kindly ask what exactly happened.