I am an American living in Australia and we do not need to see a Psychiatrist to get antidepressants over here. My local GP can give them to me, or any Specialist. However I have been on several of them and they never helped my pain at all, and I had bad side effects from them. Perhaps they do help some patients, but not all.
I was referred to a psychiatrist when my "flailing limb syndrome" started. My neurologist didn't know what it was, so he figured it was all in my head.
In my experience with emotionally disturbed children, a psychiatrist is quick to use medication to solve problems, and a psychologist actually helps with the thought patterns that lead to physical symptoms.
In my opinion, if your problem is coping with your illness, a psychologist would be much more helpful than a psychiatrist. I also believe a pain management specialist is the best route to go for making sure your meds are right. Finally, I would encourage you investige homeopathic solutions that may allow you to reduce your need for medication.
I don't know if you were referred to a psychiatrist or just inquiring but just wanted to let you know that sometimes people are referred to psychiatrists because the doctors treating them don't take them seriously and think it's all in peoples heads. Not saying that this is your situation but it often happens when test results come back normal. I don't know what you take for meds. but I would think a pain management specialist might help.
Which medications are you taking ? And who prescribed them ? (PCP, rheumatologist)