Let's break this down a bit
SLAM! Eva looked around and grimaced. She didn’t mean for the book to close so loudly
Not a very interesting opening. With a first chapter you are trying to convince me to buy your book, so why open with a girl slamming a book a little too loudly?
Eva stood up and looked up and around her.
Why? Wouldn't a quick glance around do? its not like she did something horrific. Also awkward phrasing.
To her surprise everyone else in the library had already left, except for herself and the library clerk, which was hunched over his computer.
Are library clerks inanimate objects now. Try "library clerk, hunched over his computer."
“Shhhhhhhhhhhhhhhhhhh, this is a library you know!” The clerk yelled at her sarcastically, not even looking in her direction.
This does not sound like something someone would actually say. Also it isn't sarcastic. In general never tell the reader how someone feels or their tone. Strong prose should convey this.
Eva nodded her head and giggled to herself a little.
This is problematic, it instantly starts to make me dislike the character, because other than being a not so nice person I don't understand why she is giggling (Your next lines imply it is because she is mocking him. But you haven't made him enough of a dick for me to side with her when she begins her mocking.
The library clerk was your stereotypical nerd. He wore his hair slicked back with large, thick rimmed glasses. His wrist showcased a shiny and very expensive looking, gold, Harry Potter watch with magic wands for the clock hands. He was completely engulfed in an intense game of World of Wizardry on his desktop computer.
First don't summarize something and give us details. You have to let readers draw their own conclusions. You make sure they draw the conclusions you want them to draw, by giving them the correct details. Next, point of view matters. Here you have broken it. You aren't writing 3rd person omniscent, because otherwise we would know the clerk's name, and the narration wouldn't be so seeded with Eva's perspective. Therefore, you can't include details Eva wouldn't know. For example, the watch. She doesn't know the clerk's name, but she knows what he is playing on his computer and the minute details of his watch (Also do watches like this, expensive outsides with merchandise insides really exist? Because as a reader I'm skeptical
Eva looked down at her own watch.
If you are going to spend so much time on a stranger's watch you at least think she would have some opinion on her own.
And you go on for another paragraph worth of text without introducing a plot. Which means by that point you will have lost the majority of your readers. I read the rest and was not impressed. I'm sorry to say this, but at this point your writing is very bad. You aren't going to get much out of posting it for critique here, because there is too much wrong with it to really give a wholesome critique. THAT SAID DO NOT STOP WRITING. I know this may be disheartening. When I first started I thought my writing was really good. It wasn't and it hurt when people told me so. You will get better, but you have to work at it. Listen to Writing Excuses, read novels you really like closely to see how their writers practice their craft, critique other people's work (Seems crazy that anyone who is not an expert is qualified to do this, but as a reader you just know, plus it gives you practice pulling apart prose).
Best of luck.