I had to look up Cervical Lymphedema and the only thing that came up was Lymphedema. Did your daughter have cervical cancer? Lymphedema is a swelling of the lymph nodes and can be a secondary issue caused by radiation from having had cancer so I am confused by the Cervical aspect. Can you explain exactly what is wrong with your daughter? Or maybe you wrote that down wrong? In any event one of the biggest symptoms is swelling. If she hasn't had cancer then it could be that she has a hereditary form of Lymphedema so read up on it to understand what is going on.
If she has a nodule on her thyroid that could also be causing the problem so you may want to see an endocrinologist to get a full work up besides the simple blood tests considering she has so many symptoms.
As for the POTS that has more to do with the central nervous system I believe. More of a problem with the brain regulating heart rate and blood pressure as opposed to being a direct problem with the heart. Compression socks can help. If her sodium is not out of line she can try and take in more sodium. Exercising depletes the body of sodium as well drinking a lot of fluids can also deplete sodium so though water is really good for the heart, it helps it function better and is needed, if she drinks a lot of it and has a very low sodium healthy diet she may be struggling with low bp related to low sodium levels. So adding a few salty snacks may help her feel a bit better.
Other than that I might suggest seeing an immunologist. She has some varied symptoms that might suggest Lupus. I am not saying she has it, she would need to be tested by a doctor but I would take her to get it ruled out.
Please do keep in mind I am not a doctor so this is all based on my own research but sometimes having an outside perspective can help so hopefully I have given you a few new things to think about. But you really need to see a doctor to get a true diagnosis and unfortunately it sometimes takes multiple doctors of different specialties to get to the bottom of things. It definitely does not sound like your daughter has typical symptoms so keep following your gut on it and do not let the doctors write her off as simple allergies until you have exhausted all avenues. Best of luck getting this sorted out. You may want to also post your question in the Undiagnosed Symptoms forum
http://www.medhelp.org/forums/Undiagnosed-Symptoms/show/95 and see if there is someone there who might have some thoughts. Take care and keep us posted on how she is doing.