How would I say it well that I moved out of my house and transferred to another apartment...?
I moved out to an apartment from my house.
--not a teacher
I have just moved into a new apartment, guys.
_ And what do you call the feeling, some uncomfortable feeling of staying in a new place?
You were looking for a word to express the discomfort of being in a new place - since nothing is where it should be, I feel that I would be unsettled.
On the other hand, you might well be feeling elated at a successful move.