You problem sums up three different problems: 1) First, you like this girl, but are unsure if she likes you or not. 2) Summer holidays, and she is unreachable, which makes you worried if someone else might snag her. 3) You don't have her number.
How do you get a Girl's phone number? Let us say, it's just about the number, in how many ways is it possible?
1) You chat with her often. She likes you and vice versa, and it happens. (the most common)
2) You chat with her, ask her what she does, and after she tells you, you go crazy and type - "what? really? I don't believe this!!", then you ask more about what is she doing in that field such as - college, which year, work, et cetera; and when she asks you 'why are you so interested?', you reply: - To be honest, I was actually looking for a _____ (whatever she does) for my newest book...and I am completely awe-struck right now. - I was just reading about _______ (whatever she does), and I found you guys so awesome. It's such an honor/ It's so great/ it's absolutely exciting to meet you. Tell me more about your work! - (if you are earning) Well, actually a friend of mine just happens to be in this project (link it with whatever she does and make it as big as you can)
3) Search her friend, pick the most romantic movie of all times and copy paste the most effect-making dialogues from that movie in front of her, be a gentleman to her, and you'll have it.
And there are many more, but in this problem, they are not needed.
Furthermore, because you have no time as waiting for her to come back can be pretty risky, I suggest you look for two things: - See if she comes online on facebook/ messenger often or not. - A friend of hers who is reachable.
You'll have to play the confession game with her, be as ultra romantic you can be in front of her friend, don't be cocky. And because now she will be prepared and aware of the fact you have feelings for her, your just saying 'That I want you to be my girl', or 'I love you', or ... won't be enough. Dazzle her with a surprise, like write her letters, or a song for her, or anything that will surprise her romantically.
Ps: If you can, write her letters on Facebook, so when she opens her account, she gets surprised that all this while you were missing her and your letters will do the rest. (Just pay some writer- friend to write you 10- 15 awesome love letters) (Post your relationship problems here)