Thanks for your replies guys. This is really helpful and inspiring. But the truth is, right now, I can't leave the house because of both family and financial reasons. My mom gets nervous and my dad becomes restless even if I go out after 6 pm with my friends. It will take time for them to give me that much of freedom.
My parents are not keeping me as hostage or in their control. Apart from this issue, I am quite independent person and have a good time with my sister, dad and sometimes even with my mom.
Also, I can't leave my mom in the emotional state that she is in. She is already going through identity crisis since my sister left and if I ask to leave too, she might completely break down.
What I need is some help on how to make sure that my mom is out of this depression. I know therapy is an option, but I need to first get her out of this "rage and annoyance" state to get her to see that she needs help.