A.J.
Ooof! Hard! Sounds like you got in the habit of responding right away, so now she's used to it.
I always use the "I almost never carry my phone" excuse (but for me it's true) and for certain people, I ALWAYS take a while to answer emails, etc just to "pace them" from not contacting me more..you know?
Limit her FB viewing with privacy settings. She won't know. Say you haven't been logging on much.
Maybe say, "Hey, I need to talk to you about something, and it's sort of awkward-this has never happened to me before. You're such a great friend and neighbor, and we got familiar so fast, that suddenly I'm socializing and communicating WAY MORE than I can handle. I've always needed time to myself with my family. Can schedule ply times for X times (once or twice per week) That would work much better for me."
Don't acknowledge the phone comments, just simply don't respond every time or right away to texts. If she presses, say, "I do not always have my phone." Don't cut her off, just maintain the amount of messages you are comfortable with.
She may get miffed, but you haven't done anything wrong, and if she blows up or something, you have an excuse to cut her off...which my be good in the end. She sounds super impossible to handle!