In some states, it’s illegal to get private testing.
However, I’d urge you to find a doctor who is willing and able to get to the source of your obviously physical issues. Several years ago when traveling, I collapsed and wound up in the ER of a local hospital. Tests indicated severe dehydration but no reason for it. When I returned home, my now ex-primary wasn’t interested in finding the cause of my collapse, since it was ‘resolved.’ My endo, however (I’m hypothyroid), not only ran some tests but also referred me to a urologist and a nephrologist to try to find the cause.
My point is that many doctors will not do much if the patient’s issue is complex and difficult to identify. You need to find a doctor who is like my endo and interested in the patient’s well being.