Welcome to the board. I'm sorry you are having so much trouble, but that isn't too unusual.
First of all, the cpap does not make you breathe, and it should not change how you breathe. CPAPs blow a steady pressure to splint your airway open. If your machine is set for c-flex (respironics machines) or the equivalent, it will decrease the pressure somewhat when you start to exhale, and then increase again as you inhale. If your machine is an apap, then the pressure may go up when it senses you are having an apnea event. We can tell you more once you register and let us know which machine you are using.
Panic usually comes from feeling out of control, such as when you sense the machine is trying to control your breathing. Plus it takes a bit of psychological adapting to knowing you are dependent upon the darn thing, and to sleeping connected to a hose, and wearing a mask, and the whole shebang.
One way to deal with it is to use the machine while you are relaxed (good luck with that!) and awake, possibly in a room other than your bedroom. Use it while watching tv, or listening to music, just to get a feel for it, to realize that you ARE still in control, and that it's not the end of the world to have to use it. When you put it on at bedtime, and if/when you wake up during the night, do some relaxation exercise (meditate, pray, repeat a mantra, sing a song in your head, etc.). If you have a panic attack during the night, DO NOT give yourself permission to sleep the rest of the night without it. Do you have children or know any? Remember how they have to learn to sleep alone through the night? It's the same principal learning to sleep with cpap - just keep plugging away, with a little reassurance and reminding yourself that it's for the best.
If yourmouth keeps popping open, you may want to consider a chin strap.