That does seem worth checking out.

My first thoughts are that you may have an enlarged thyroid gland or thymus (in the chest). Also I have read that a prolapsed mitral valve in the heart, makes lying on the back difficult and symptomatic.

I'd ask the doctor to check for long QT syndrome(heart). Amitriptyline is a drug which can make this worse, and it is potentially serious. (and sometimes deadly)

Amitriptyline also causes dry mouth and throat. You might try a drug free period, to test this out as well.

Drugs always have a dark side, and should be evaluated always when problems occur like this.