Updated iPhone, forgot Apple ID password, can't log in

I updated my iPhone 6 last month, and when I did so, it logged me out of Apple ID. Now, I can't remember the password.

When I try to change the password, I get a message saying that a notfication will be sent to the phone with instructions, but that notification never arrives. My iPhone is bugging me about entering my Apple ID password every 15 seconds or so. It's driving me crazy.

How do I get this password reset if I don't get the reset notifications? Help!