I actually know the answer to this.
It's the body's way of keeping the plumbing working. Your penis is full of blood vessels that create the erection and morning wood is just your body's natural way of exercising the 'pipes' while the rest of you is out cold.
I know it's embarrassing for you, but your mom knows about morning wood because your dad gets it all the time. Now, perhaps, she will be more cautious about coming into your room to wake you, knowing that you are now to the point where you are becoming a man.
Speaking of becoming a man, maybe now is a good time to start taking on some adult responsibility, Get yourself an alarm clock and start getting yourself out of bed in the morning. Morning wood is going to happen and if you are going to go to sleep paranoid about her coming in, you aren't going to sleep as well.