A genetic counselor or clinic should be able to run some tests for EDS, but a lot of them just go on clinical findings, as they have not pinpointed genes for ALL forms of EDS. Also, I don't think there is a direct link between EDS and POTS. That is, lots of us with EDS also have POTS, but I don't think anyone has shown definitively that EDS causes POTS. So there's no genetic test for that.
It's also possible you could have a genetic predisposition for autoimmune diseases which lead to POTS, and researchers definitely have not found all the genes responsible for autoimmune diseases.
Certainly, if you have official Familial Dysautonomia, that can be tested at a genetics clinic. People usually know their kids have that at a very young age, though, so that's unlikely.
Have you read through the Health Pages info on these causes?
http://www.medhelp.org/health_pages/Neurological-Disorders/Genetics-Relating-to-Dysautonomias/show/832?cid=196
When we were in Cleveland, we were asked to participate in a study. They believe my son's POTS and autonomic neuropathy are hereditary. All the members in our immediate family,Grandmother,Parents and Children, have a lengthy medical questionaire to fill out. They will also collect a saliva sample as well. This is through his neurologist.
After completing the questionaire, I believe, it is comimg from my side of the family. My mother, sister and I have all had bad migraines. When I was young, I would often get what we called 'head rushes', but never fainted. My brother says he still experiences frequent head rushes. A couple of years ago, I passed out at the post office when I had been waiting in line for 20 minutes, not moving. The doctors couldn't figure out why, but since I haven't done it since, Nor have I returned to that Post Office (how embarassing), I didn't think much of it.
During the Tilt Table Test, my sons legs turned deep red(purple).
Anyway, I believe they can just do a saliva sample. This testing is being done by the neurologist.