Hi White,
She is most likely just being friendly.
In the past 15 days, she may have been initiating conversations, looking you in the eye without looking away and laughing at what you say because she wants to get your attention again.
This is especially true if there is a guy that she was recently dating or talking to who is no longer in the picture.
In essence, she no longer has the kind of male attention that she has probably been getting in the last several months.
Being that she already has some history with you and knows that you asked her out in the past, she may be acting so attentive towards you all of a sudden because she is hoping to get attention from you in return.
However, given how she has behaved in the last few months in avoiding you, there is a good chance that if you start giving her the attention that she is most likely seeking from you, she will eventually become satisfied and decide to start avoiding you again.
You have asked her out in the past and she rejected you.
Even though you believe that she was trying to get your attention right after the rejection and you have also since noticed her looking at you from a distance but immediately looking away once you catch her, it is still unlikely that she is interested in you.
She may have been trying to get your attention right after she rejected you because she was trying to gauge your reaction so as to determine whether the friendship was now damaged.
Once she noticed that you were keeping your distance, she decided to do the same.
However, you may be catching her looking at you from a distance because there is still a part of her that misses her friendship with you and reminisces about how it used to be between the both of you.
She may miss the lunches and conversations that the both of you used to have.
However, none of this definitively denotes romantic interest.
It may simply be a sense of loss that she feels and thereby she becomes compelled to look at you.
A strong way to learn that she is into you is if she starts flirting with you constantly and tries to get close to you physically whenever she is interacting with you.
She may even touch you often without any good reason.
She may ask about whether you are dating anyone.
Also, she may ask for your social media.
Consequently, you may notice that she is following all of your stories on social media and liking a lot of your photos.