“Aloud” is the more formal version of “out loud.” Feel free to use it in your essays for school.
As far as “out loud” is concerned, it is a perfectly legitimate word that can be used on Tumblr, Twitter, Facebook, text messages, and in other informal settings.
Don’t worry: not many teachers—if any—will think less of you for choosing to use “out loud” instead of “aloud.”
Having said that, since “out loud” is so mainstream, show your hipster diction by employing “aloud” in your writing.
That’s all there is to it.