To faze is to disturb, bother, or embarrass, but a phase is a stage or step. It could faze your family if your princess phase lasts well into your college years. 

Faze entered English around 1830 through American English as a variant of feeze, to mean "frighten." It's often in the negative, like when your mellow brother is unfazed by your crazy Cinderella costumes. Don't let these examples faze you:

Gasser didn't seem fazed by his teammates' early shooting woes. (Seattle Times)

Morgan doesn't seem fazed by Google overwhelming influence in the tech world. (Forbes)

A phase is a stage, like the phases of the moon or the awkward phase of teenage rebellion. As a verb, it means to do something in stages, like to phase something in or out:

Education officials are now considering phasing out the middle school grades and possibly housing a new district or charter middle school in the same building. (New York Times)

We will finish Phase One, and then we will look at Phase Two," says Peter Voser, Shell's chief executive officer. (Business Week)

I never know if musicians see bands going through all these different phases the way outsiders or music critics do. (Time)

Confusing phase for faze is an error that usage guru Bryan Garner notes as being at stage 2 of language change: having spread to a "significant fraction of the language community" but remaining "unacceptable in standard usage." So don't get them mixed up.

To keep them straight: something that fazes or bothers you might make you want to fight, but please pass through your princess phase as soon as possible.