Which is correct: I'll be moving next month or I'll be shifting next month?
In American and British English, "to move" is the standard verb to express the idea of relocating one's belongings from one dwelling to another (among other connotations):
I moved from Baker Street to High Street.
"To shift," when referring to objects, generally has more of a temporal sense associated with it:
I shifted my class from Monday to Wednesday.
or an internal reorganization:
I shifted the remaining funds from renovations to education.