Need suggestions and opinions on my situation.

I'm a guy in grade 12. There's this cute girl who's in my grade and I've known her for a while, we've had a few classes together in grade 11 and I got to know her a little bit more and ended up liking her a lot, but she never really knew as I'm shy and and never really showed it. Now fast forward to grade 12, I started talking to this girl again and I'm 90% sure she likes me. We started to talk more and I got to know her friends, one of her friends knows that I like her a lot and is helping me out a bit lol. Her friend told me I should join the school's eco club to maybe talk to her a bit more as the only class we have together currently is Calculus and we don't really sit close together or have time in class to chat. So I joined the club, having hopes of maybe getting closer to her, I ended up going to her house with her friends to paint a sign, she wanted to drive me home after and I wanted to ask her out to lunch so I did when we got to my house and I asked her to lunch, she said yes.

The next day we went to lunch and I realized she's extremely shy and quiet, she isn't that talkative and I tried hard to keep the conversation going, lunch was pretty good in my opinion and we made plans to hang out on friday after school.

We got to hang out yesterday (friday) as we planned to watch a movie after school. She's really quite and shy and dosent really have an opinion when it comes to things as I asked her what she wanted to do when I was over and she kept on saying 'whatever you want to do, I want to do what you want to do' and she kept on asking if I was having an ok time and if I was getting bored, etc. I guess we both just go along with what the other person wants and yeah I didn't want to screw it up or make it awkward. After a bit we decided to watch a movie as the movie we planned to watch at the theatres starts at 7 and it was 3 at the time (she really likes movies and she watches movies with her friends a lot).

Anyways, we ended up going to her room and we sat on her bed leaning against the wall with her comforters against the wall as support. We ended up sitting pretty close to each other and we were in a comfortable position, I was holding the laptop and we decided on watching White Chicks lol. I don't remember how but she ended up putting her head on my shoulder and I kinda leaned on her head. I instantly started to get nervous, and if she saw my face it would have been pitched red. My heart was pounding and I tried to take deep breaths with out her noticing, don't laugh but yeah I loved every bit of the moment, and part of her hand ended up touching my arm. Throughout the movie she ended up having her leg bent and over mine and asked me several times if I was having fun and she hoped it wasn't boring, she also told me this is the first time that she's had a guy in her room and I could tell she was kinda nervous. She said she was kinda cold later so I asked if she wanted to like get some more clothes or something but she said no. Was this a sign to wrap my arm around her as her head was already on my shoulder and believe me I wanted to but I didn't want to scare her or rush things, and kept on saying no to my self. Should I have just maned up and put my arm around her?

We left for the movies and we watched Olympus has Fallen, but basically we didn't talk that much during the movie and she was really close to me like leaning on my side and I was leaning to her side, I wanted to wrap my arm around her but lol it would have been so cheesy if I did at a theatre, and I guess I was really scared and kept on telling myself it would be a bad idea.

After the movie she drove me home. I don't think it was awkward, just we didn't talk as much as I thought we would have, mainly because I think we're both really shy and both just wanted to do what the other person wanted to do. I can't stop thinking about that day and keep on over analyzing everything, hating my self for making it awkward and how I might have screwed it up or something.

I want to hang out with her again, and get to know her.

How do you get shy girls to talk more, more so one that dosent have anything she wants to do and wants to do what you want to do.

I really really like this girl and I want to ask her out to prom, I think we both want to go with each other to prom. I want to ask her out again maybe just to hangout at her house again and watch a movie, but I don't know if she wants to.

How should I get closer to her?

Sorry for the long story, lol.