Hey OP, I'm by no means an expert but I know very well how miserable facial pain is. I've been suffering constant facial pain, with bouts of extreme facial agony, for four years. Like yours mine varied, sometimes really tender, sometimes less so. Over that time I've had a number of diagnosis and theories from the GP and other doctors, starting with dental infection (had root canal, didn't work), sinus problem (had medication, didn't work, had surgery, didn't work), neuralgia (had medication, didn't work) but it was a consultant neurologist who eventually diagnosed me with chronic migraines.
I'm not saying this is what you have, but if you haven't seen a neurologist, I think you should go to your GP and insist on a referral. If it is neuralgia, and what your GP has prescribed isn't working, you need to see a neurologist anyway. I'm so glad I did, I'm not pain free (yet) but the neurologist's treatment has made so much difference already, it's not perfect but it's so much less miserable.
Also, are you still taking the amitriptylene? Isn't that something you take daily, rather than 'when needed' like paracetamol or something? I could be wrong though, I have taken it in the past but it turns out my body hates it so I came off it again in a hurry...