“I’m dying to take a shower” basically just means you really want a shower. It is usually used as a dramatic way of expressing desire for something. We also say “I’d die for ......” or “I’d kill for.....”, and i
I’m dying for a break.
I’d die for a nice cold glass of lemonade right about now.
I’d kill a man for a nice cold beer.
It’s almost never literal, so don’t worry too much. ;)