When we apply force to make a tooth move, two main processes take place in the bone around its root. On the side towards which we want the tooth to move, the bone is resorbed (broken down), and on the opposite side new bone forms. It takes between 3 and 6 months for new bone of sufficient hardness to form, but during that time we keep moving the tooth in the desired direction. The further a tooth has to move – the greater the distance from its starting position to its final one – the longer the bone around it stays softer, because it's at different stages of hardening. During this period the tooth may feel loose. Not every patient feels this, and not in every tooth. The process is normal: once the teeth have finished moving, the bone forms and hardens, and the teeth stop feeling unstable.
This answer is for general information. Your own case needs an examination by an orthodontist.