It's always situations like these that people tend to leave out stuff and just tell part of the story to make things go their way (not saying you are mind you).
I've worked with a lot of small childeren and the most common thing that happens is "johnny hit me" and he's all crying and stuff trying to get this other kid in trouble thinking he's hella clutch and then the other kid is screaming like a maniac with a big welt on his face. I mean, no stuff he hit you, you whiny bitch it looks like you knocked him in the face with a wrench. It usually helps your case if you tell the WHOLE story, if you start out lying, obviously the moms going to believe the small child who is screaming and crying telling a whole different story.
And I realize you are young and may have anger issues or something but holy stuff no reason to be a little bitch and run up to your room and mope about. Then whe your mom tells you to open the door after you (most likely, positively) slammed it, you make up and excuse of "i thought she wanted the cat in".
What kind of bullstuff is that, she said open the loving door not "the cat wants into your room". And even a second time you do the same thing and crack it open only a little bit. I would have cussed the stuff out of you.
You may have problems with your mother but honestly, arguing with her over something as stupid as that is just stupid and isn't going to help either of you. It usually helps to act your age.
just my two cents idk