Let me start by saying that I've only read the first few chapters of this, but they've actually intrigued me pretty well. That doesn't always happen in the opening chapters, so good job :) The voice of your mysterious texter is natural and flows pretty well, for the most part.
-I've noticed that you sometimes use unnecessary commas in the non-texting parts. For instance, "I say, looking at my phone, expecting a reply, wanting one, in fact." This makes for a really choppy sentence. I recommend breaking it up into smaller sentences or combining some of the clauses. Maybe something like, "I say, looking at my phone, surprised to find myself expecting and wanting a reply."
-In a few spots in chapter one, you forgot to unbold a few lines that weren't texts.
-I also noticed that you have a tendency to state things, rather than show them. Instead of saying "I always like looking at the new phones and tablets." you could demonstrate with something like, "I drifted over to the section with the new phones and tablets, like I always did. Looking at them longingly, I wondered which would be the next on the growing list of devices I wanted to save up for."
-If at all possible, try to avoid putting things in parentheses.
-I found the conversation between the main character and Tyler in the car to be a bit awkward, a bit unnatural. I don't think it's particularly plausible that he would ask her to count how many messages she sent to this random person. In addition, it would more natural for her to lie and say she was texting a friend from school, probably a girl. Unless she doesn't have any friends, I don't know.
-In chapter three particularly, be sure to break up long paragraphs into smaller ones. Blocks of text can sometimes be intimidating or off-putting to readers.
All in all, though, you seem to be doing pretty good! If I get a chance, I'll read the rest, but in the meantime, keep it up :)