Do public college students hate rich kids?

I'm going to college soon and I'm absolutely terrified of what they'll think of me. I really want to go to a public college in California to experience the "normal" life--as my mom puts it--so mostly CSUs because she said that I have to learn.

I've been in private schools all my life, I have a maid and a driver, an iPhone 5s, Xbox, Wii, DSi, and a Macbook Retina that's covered in pink rhinestones and crystals with my name. I have also never used the washing machine, cooked or ironed anything because my mom says that I will break/ruin things. To make it worse, my parents are buying me my own BMW for college. Even though my life sounds really nice, it's not because my parents don't pay attention to me because of work and they think they make everything up by buying me things. I also didn't have many friends growing up because my mom never let me out because she said that I could be kidnapped and that they'd only like me for my money. It sounds ultra cliche and fake, but this is actually true.

I'm not arrogant at all and I never show off; I actually have a very low self-esteem because I barely had any friends and I'm very shy. My "popular" sister also calls me a total loser because I'm in love with anime, manga, and video games.

Do you think that the other public university students will hate me? I'm trying to change by learning how to cook, but it's not going very well. It's because I don't want "friends" that only like me for my--well, my parents'--money. I want to have friends, but I'm scared that they'll think I'm this stuck-up, arrogant girl.

What should I change about myself? Please bear in mind that my mom will not let me handle the house chores because she says that they'll "ruin" my hands, so they'll be rough, and therefore I have absolutely zero life experience until I actually reach college.

Nobody will like you because of your money. Nobody else cares that you have money, they are concerned with their own financial situations.
Use college as an opportunity to experience what your parents denied you. Do your own laundry, cleaning and cooking. You will learn quickly, it's really not that hard. Most college students survive on junk food anyway.
Leave behind the rhinestones or any expensive items that might be stolen. Don't wear $500 shoes or designer clothing, dress like a normal college student. Do these things and you will fit in just fine.

"To make it worse, my parents are buying me my own BMW for college."

You realize you're allowed to say no to them buying you stuff, right? Or to tell them that you really appreciate the gesture, but you'd like something a little less flashy?

Frankly, I can't understand why you're being allowed to go to college at all if your mom's so terrified for your safety, let alone why she's made this sudden 180 on you having to learn how to fend for yourself. Use that as a starting point for why you need to start doing your own cooking/laundry/cleaning/etc.: because if you don't have the chance to make mistakes and correct them now, it'll be ten times harder when you're on your own. Recognizing that you are privileged is an important component of not coming across as a spoiled rich kid, but being able to function like a person who's never had those privileges is an even more important step.

As long as you don't have an ego and flaunt your money you'll be fine. College is a great way to become independent. I was shy too when I went to college, but I put myself out of my comfort zone and joined some clubs, and campus events. I made some good friends. Just smile and be (or at least look) happy and people will talk to you. College will be the best time.