You know you are not faking, but you are really confused: why do the standard treatments not work very well? And when are you finally gong to get a decent night's sleep?
I shall start at the beginning and work my way around to your question. Pain is a signal from the brain to the body to stop doing what it is doing because something is wrong. Most of the time, this is a good system. You do not walk on a broken leg until it is set. You take your hand off the hot stove and treat the burn. You go to the doctor when your stomach hurts and find out why. Pain tells you something is off and you get it taken care of.
A grey area exists after you have gotten treatment or discovered why you have a headache. The pain persists to remind you to be careful. Most of the time this is useful--you do not want to re-injure yourself nor do you want to overdo something after surgery. On the other hand, these are things you can figure out on your own and perhaps get help to minimize the pain. That is why it is ok to take pain medications after you have had the issue diagnosed and especially after it has been treated, but has not fully resolved.
So far, so good. But your pain, you say, has been treated, and nothing more is wrong that a doctor can discern, but it has not at all gone away. This is where that referral for psychology comes in. NOT because "it is all in your head", but because it is all in your head! To be clear, all pain comes from your brain, right? But if the pain in the brain did not subside with proper treatment, then the brain is signalling something is still wrong. Now the something is more difficult to discern, because the causal link is not clear. A broken leg gives you leg pain. This pain might be in your leg, your back, or your shoulder, but apparently that does not mean you have a problem in your leg, back, or shoulder this time.
