Hanged your shirt just doesn’t make sense.

You can not say, I hanged my shirt, if you are using correct English. You can say your shirt was hanged if you wish, but not or that you hanged it (speaking to someone else who has performed that service for you) but you can’t say I hanged it.

Sorry – sometimes teachers are wrong, other times memories are faulty.

it takes getting to know the difference, based on the context, how they are used.

“Hanged: they hanged the man at dawn.”

“Hung: I hung my pants in the closet.”

“Hanged” is used exclusively when referring to capital punishment (“hanging” by noose).