How do I convince my desi parents to let me move out?

For starters, I [F22] have been battling with depression and anxiety for a few years now. It's recently started getting worse as my older brother [M26] moved two hours away for law school. He's my mom's favorite so I think it's slowly making her more...you know, crazy.

I come from a strict Gujarati-Hindu family. My parents are in their 60's and can manage to live alone by themselves. So, why do I feel obligated to stay at home? Why do I feel guilty about thinking of moving out?

I get home from school late in the evenings. My mom constantly accuses me of silly things. "You're not really going to school - you're out having sex or with your [nonexistent] boyfriend!" I can't stand living at home anymore. My parents have always fought since I was a kid, and it's hard to study here. The other day I went out to Starbucks to read my books and I got scolded for leaving the house. I get bad anxiety from simply being around my mom, or even hearing her voice first thing in the morning.

I recently found out I have macrocytosis, so my red blood cells are larger than normal and I have to get more blood tests to figure out why. When I told my parents this, my mom immediately blamed me and said it was my fault because I've been "eating junk food" every day (lies). My dad, thankfully, stood up for me and said that I eat the healthiest out of everyone in the family. I don't know, I keep picturing the disgusted and apathetic look my mom had on her face when I told her this news. It kind of broke my heart. Every day when I come home from school or work it's another accusation or irrational scolding from her. She'll stare at me and give me dirty looks.

The only place I can move out is within the same city. I go to college about 10 minutes away from my parent's house. My closest friend since high school has her own apartment, which is less than 5 minutes away from my school, and she said I can move in with her.

tl;dr I'm terrified of all the excuses my mom will make as to why I don't need to move out. Even though I'm an adult, I feel like I'm forever a prisoner to this house. My anxiety cripples me. I know the easiest answer would be: just pack your things, tell your parents you're moving in with a friend (that they know of/met), and leave. I know that this may possibly cause a potential argument between my parents. But it's not that simple. I feel like so many cultural values play into this, and I feel so much guilt.

Please, any advice.