Cassie,
The feeling of not getting enough air when you breath, usually accompanied by a "yawning" is referred to as "air hunger". This is brought on by anxiety. I had loads of this.
As far as the swaying, I have felt dizziness, or rather off balance before, but I wonder if the rocking at the computer or while sitting is not giving you a motion type sickness, which in return is frightening to us with panic.
Most of all, lack of sleep or interrupted sleep will heighten anyone's anxiety.
Try to stick to a strict bedtime schedule, hot bath, drink some chammoille tea, read for 20 mins, then bedtime, at first you may only notice extra 10-15 mins sleep, but it will get longer and less interrupted.
I find walking early evening or late afternoon helps to de-stress the body, it also regulates your breathing.
Trish