Originally Posted by carlosdca

actually it is the opposite.
The OP said it was the cheap bag you get at the store.
I have bought suits at Macy's and they come in a long black sleeve with the hook of the hanger sticking out at the top.
They actually don't have any device or strap to make it foldable (unlike the real garment bags).
They look like a garment bag and it is actually a garment in a bag, which does count as an item for air travel purposes.

If the OP was willing to fold his garment in four and put it in his carry on bag, he would have done it before arriving to the airport.
BTW, I do fold my suits and pack them in a roller bag using the method described below. It has worked pretty well for me without pressing needed at destination.
Video title: "In Depth How To Fold A Jacket For Any Trip No Wrinkles Best Slow Motion"
Instructions start around the 1:38 mark.
https://youtu.be/gQFwepmvL7A