You're not sick and twisted, you're just a confused kid. At your age you're getting lots of hormones through your body every day and your system isn't used to it yet. That means its easy to spin out of control. And if you've other problems on top of that, then the loss of control can be very scary. But you're obviously aware that you did the wrong thing, and you want to say sorry, so you're not sick and twisted.
How to do it depends on what kind of people you and your mother are. I keep track of what I need to say better if I write or type it. I lose my explanation if I speak sometimes, especially if I'm upset. But maybe speaking would suit you better - like I said, it depends on what suits your family. Unless you want to try a new way, of course. Just be sincere and admit how strange you felt when you got mad, and maybe she'll remember how weird and strange she felt at your age too!