Also I wonder if you call it its re-branded name: Post infectious autoimmune encephalopathy, will remove the paediatric part (assuming your older) as I think PANS/PANDAS tends to limit the group it affects, my apologies if this is unhelpful, i understand your desperation, I would try the private route.
I've attached a paper about auto immune encephalopathy, in it, it describes a number of auto immune anti-bodies as well as the offending infections in this condition, it relates to paeds but equally applicable to adults. If you are able to identify with your GP any of the antibodies for the infections you might just be able to get a decent enough neurologist to acknowledge. My son has current infection for mycoplasma pneumoniae has abx but no doctor to provide ongoing treatment.
The research was carried out in England
http://jnnp.bmj.com/content/84/7/748.full