How do I be myself in front of a friend

We have a new person in our class, and I immediately liked her so much (not romantically) so I hung out with her. And for some reason I always want to try and impress her or pretend to be cool. I try to refrain from actually pretending to be someone she can have fun with, but it's still just like??? I don't know I hate it. She doesn't need me, but I feel like I need her. I spend the rest of the day repeating my memories with her over and over again, hoping I wasn't awkward and hoping that she doesn't dislike me. I'm almost like her complete opposite, she's blunt whereas I'm pretty shy. She's strong and I'm weak (I don't mean this as a "quirky" thing, I once fainted in the shower and I was close to fainting at school, and I barely work out anyway) but I really want her to like me. We're both introverts and watch anime though, but so far I think those are the only things we have similar to each other. 

I was also thinking for two days about asking for any type of way I can talk to her (WhatsApp, Instagram, etc.) but at the same time I fear that she wouldn't want to. I don't want to make her uncomfortable, but my own overthinking is making me uncomfortable. I want to make her happy, but I spend so much time thinking about it that I probably haven't made any progress at all. And I also don't want to go overboard. She said that she loves stars, so I'm planning on learning how to do a paper star for her, or maybe fill an empty jar with paper stars for her, but I've only known her for three days. Why am I like this? I hate it.