Shift vs Move
I remember editing an academic book on the development of Malaysian and Singaporean English. One of the words that the writer had discussed was the use of the word shift. Here in Singapore, we tend to say things like:
I've shifted house.
I'm shifting.
The better word to use in these cases is move. I've moved house. I'm moving. Move does carry the meaning of changing your place of residence. To say that I'm shifting house, sounds as if you're moving the entire house to a new location.
Strictly speaking, shift does carry some of the same definition as move but it's a poor choice of word. When you're talking about changing the place where you stay, it's better to use move.