Oh my, I feel for you.
Having been through a search for a diagnosis for my own child (different situation–hers was health problems and accompanying serious depression triggered by a concussion) I can say that searching for a key to the health issues should be a primary goal (although I know you can’t ignore the behavioral piece at the same time–it is hard to balance the big picture with immediate relief) While we were looking for health solutions, my child was on psychiatric meds and getting therapy.
To find a psychiatrist and explore medication, ask your pediatrician for a recommendation, and be willing to pay for out-of-network in order to get quality care (we did this and were able to get reimbursed for much of it by our insurance company–you can check this beforehand)
I second the suggestion to check out PANDAS above.
Our experience was that conventional medical practitioners were not helpful. Everyone only looked at their little piece of the picture, which was never enough to get any results. The end was when I needed to argue with our pediatrician to get her to do a Lyme test. We ended up heading to an integrative medicine practice (with a board-certified doctor, though). This doctor was willing to cast a wide net and test for everything, which did turn up a problem (adrenal insufficiency) that explained many of her symptoms and was something rare enough that no one would have looked for it. Treatment for this led to improvement (but not elimination) of her issues so we ultimately went to another practitioner (“functional medicine”) who looked at leaky gut/microbiome health. Following his protocol has changed my child and led her back to physical health.
I am not saying that seeing a functional medicine practice will help your child as it did mine, just something to consider as an option.
I did share this just because, despite my firm belief in conventional medicine, I needed to go outside of that system to find the help my child needed. It was expensive (all of these practices are ‘out of network’–you may be able to get some reimbursement from your insurance company if you file a claim) but worth it in the end. And if plan A does not work, be willing to head to plan B, C and D until you find a solution that works. And it may end up being a combination of plans, A, B and C that works for your family.
Much good luck in your search for help and answers.