Dysmorphia is derived from two Greek roots.

"Dys" means "bad or unlucky"

"morphe" means "shape or form"

"Dysmorphia" therefore means "bad shape.

It does appear to be related as a cousin to morphine.
According to http://www.etymonline.com/index.php?term=morphine
morphine is derived from "Morpheus" the Greek god of dreams, but But "Morpheus" is also derived from morphe, presumably because in dreams we see the form of things.

If the effects of related products like oxycodone and vicodin are any indication, morphine makes one very sleepy.