The first, unintentional look is allowed, the second is not.
just make sure the first unintentional look isn't a few hours long

bro, i beg u don't talk to her in that way unless u think it's gonna go somewhere, otherwise ur just going around in circles of sin,
and if u try talking to her without any confidence, it's not likely she'll like u at all, women don't usually like men who are not in control,
again, i really liked bro ardianto's post,
if it's Allah's will for you two to unite one day, all good and Al hamdulillah.
if not, then He knows best, you won't benefit urself by stressing out about it.
and no, it's not a sin to feel an attraction to someone, Allah knows you cherish them in your hearts.
but it's definitely not easy to draw a line of what you should do and since you're that young, it's more than likely that it'll go down an avenue where you'll both lose out and draw the wrath of Allah on yourselves because you'll take a long time before you marry and it's easy to lose control when ur so close to each other physically.
best advice i can give is calm down, and see positive scenarios where you both might not end up getting together because it's not Allah's will, but if you're willing to take a step back and regain control of yourself, Allah will draw her to you in due time if that's His will or you'll find someone who you'll love more and will love u more, and her deen will be pleasing to you and to Allah.
and remember that ultimately it is Allah who controls the hearts.
Yusuf Ali:
There is no blame on you if ye make an offer of betrothal or hold it in your hearts.
Allah knows that ye cherish them in your hearts: But do not make a secret contract with them except in terms Honourable, nor resolve on the tie of marriage till the term prescribed is fulfilled. And know that Allah Knoweth what is in your hearts, and take heed of Him; and know that Allah is Oft-forgiving, Most Forbearing.
Pickthal:
There is no sin for you in that which ye proclaim or hide in your minds concerning your troth with women.
Allah knoweth that ye will remember them. But plight not your troth with women except by uttering a recognised form of words. And do not consummate the marriage until
(the term) prescribed is run. Know that Allah knoweth what is in your minds, so beware of Him; and know that Allah is Forgiving, Clement.
Quran 2:235