"Ich war hier nicht beliebt, deshalb werde ins Ausland wechseln."
"wechseln" is a strange word to use in this sentence. I would probably translate to "change": "I was not popular here, thus I will change to abroad." But I must admit my english is not perfect; it may be an even stranger choice is english than it is in german.
Also, "to move" is "umziehen" in this context, yes.