Help? My mom doesn't respect my privacy?

I'm posting here because i'm muslim, and I'm sure most of you understand how strict muslim moms are. ESPECIALLY my mom. I can NEVER close the door to my room. My little brother barges in all the time, and so does my mom. its really annoying, and when i am changing, i scream at her and she just leaves the door HALF OPEN! even still she wont let me close my door. Not when friends are over either. If i do get away with leaving my door closed for some time, when i come out, she humiliates me infront of my brothers and my grandma and makes me look vain by saying "were you busy looking at your beauty in the mirror?" in a super sarcastic voice. she wont even let me close my door when i am doing my homework. my mom talks really loud, and its hard for me to focus when the door is open, i have told her this numerous times, but she is a bad listener and doesn't listen. I told her that i was doing my homework the whole time, which i was, and i said "i sware" but she just kept swaring/cursing at me like she usually does and blamed me for just playing around on the computer. i would love to go to the library and study there, but its kind of hard for me because of my underwieght, i have to be eating constantly and i can't do that at the library. i need suggestions. what should i do, study in my patio even when it is pouring rain? she annoys the crap out of me too because she is constantly telling me to do namaaz even when it itsn't time yet.