Is your cardiologist an electrophysiologist? They usually have more familiarity with dysautonomia, although even then they don't know much. The doctor is technically correct that there's nothing wrong with her heart, but that doesn't mean her system is working! How was she diagnosed with dysautonomia? Did she have a tilt table test? Is she on any medication to treat her symptoms, such as Florinef or ProAmatine? Did the doctor tell her to increase her salt intake? These are some of the first things that should be tried to treat it, and a lot of people respond well to them. I don't know of anyone in your area, though someone here might. Here's a list of places that those of us here have gotten help:
Also, here is some information on Peripheral Neuropathy, which can be set off by a virus. Sometimes dysautonomia is actually part of a larger neuropathy problem. The good news is it usually resolves if it's from a virus.
Definitely keep an eye on your daughter in the pool. I used to swim every day, until the day my muscles simply didn't respond and I nearly drowned just trying to get to the edge of the pool. There's are a couple other considerations with the pool. The increased water pressure can help keep her blood circulating and her BP up while she's in the pool, but then the transition as she gets out and loses all that external pressure can cause her BP to drop very drastically. I used to get out and immediately lie down to avoid this. The other thing is, when the body is in water for a while, the kidneys will decrease the amount of water kept in the body, which can dehydrate her. I don't precisely understand that part; it was something my physical therapist and doctor discussed. This process can also set off her symptoms. On the other hand, the more active she can stay, the better she'll do.