I don't have a bite plane, but I do have an appliance that fits "sort-of" the same way. Mine has another purpose completely (distalizing molars), but also helps keep me from biting off my bottom brackets. It will get easier as you get used to it, but I think it is the worst part of braces. Just remember, if you can do this the rest will be easy! (or so I keep telling myself - haha)
My advice to you - pay attention when you sneeze and try to keep your teeth apart. The first time I sneezed with mine in I had to go look to see if I broke my bottom teeth - don't worry, I didn't and I don't think you will either, but it sure felt like it. Another person on here said she did the same thing with hers when she sneezed. Ouch!
I don't remember who it was, but maybe she will come forward to commiserate with you, too.
As you get used to it you will pay attention not to do things like sneeze wrong or bite down on it too hard, though. I also had a hard time sleeping at first because I couldn't get my jaw comfy without a way to put my teeth together and I still slobber SOOOOO much when it is in. I was told this would go away, but it hasn't for me. I also miss being able to bite into things, but I am not sure how much you have this problem? I have to tear anything I eat up and put it in the back to try to chew - and it is not really chewing, either - more like mushing around against the inside of my mouth with my tongue. I don't think most people wear this stuff for a very long time, so keep your eye on the prize - it is almost over even though it has just begun.
today
It is also making my teeth sore