I'd like to know more about your symptoms in terms of what you're saying of the fluctuations from day to day or hour to hour. Do the symptoms seem more dependent on these fluctuations than on your position, or is the worsening when you are upright and alleviation of symptoms when you are lying down more prevalent? If the former is the case, I would be suspicious that there are a few more things that need to be ruled out before your POTS diagnosis can be definitive, as POTS generally has the latter presentation. (Which is to say that while POTS symptoms can fluctuate over time, the more dramatic effect on symptoms should still be that which comes from change in position between upright and supine.)
If you're in the position of looking for possible other culprits for your symptoms that are less positionally-dependent but otherwise similar in presentation to POTS, one thing that ought to be ruled out is pheochromocytoma if it hasn't been already. Mastocytocis/MCAD also ought to be ruled out. Depending on your particular constellation of symptoms, there may be other possibilities.
If you're not in that boat, then it still sounds like you need to find a good doctor to oversee your POTS treatment. Where did you get diagnosed? Why isn't that doctor continuing as your treating physician for your POTS? Who is currently prescribing the beta blocker? If you need to find a new POTS doc, I would recommend an EP cardiologist as others have above, if you can find one with knowledge of dysautonomia/POTS.
Without knowing more about your signs/symptoms, it's hard to say much more. Do you have tilt table results? What are your BPs (lying/sitting/standing)? And your HRs (lying, sitting, standing)? Do you have syncope, and if so, how often? If you have syncope, what happens when you faint (orthostatic hypotension, bradycardia, tachycardia, asystole, flutter, fibrillation)? You mention anxiety, sweating, fatigue, loss of appetite ... what other symptoms do you have and which are triggered by position, exercise, or heat and which are chronic? Do you have other health conditions as well that have to be taken into consideration?
Perhaps knowing a little more about your situation I will have more insight into why your doctor started you off with just a beta blocker rather than one or more of the other POTS meds.
For me, I get sweaty & anxious when standing still... part of a response to the "orthostatic stress". Using fludrocortisone to keep blood volume up & more consistent, as well as shifting my BP higher, does help me minimize this and keep myself upright better. My BP still drops off, and my HR still goes up (Orthostatic Hypotension & POTS)... but it does so without as much disturbance... less faintness, less dizziness, less breaking out in sweat, etc.
I guess what I'm trying to say is that it is worth a shot. It isn't going to be a total cure, but there is a decent chance it will bring a more stable backdrop to your body. I know that my "hydration level" tends to fluxuate a lot on its own, and fludro helps me get to a more steady state (with less overall drinking & peeing in my case).
If you have what looks like chronic low blood volume, like dehydration symptoms much of the time, then fludro is a "first line" thing to try... if your BP is high, maybe it's not... check closely with your doc.
I think AireScottie is right to mention autoimmune issues since those can zap the thyroid along with other things and might be a root explanation... worth considering.
Generally Electrophysiologists deal with this; I'm curious about your other symptoms though. I see on your profile that you have post-viral syndrome and maybe a thyroid disorder. What did your Rheumy and Neurologist come up with? I ask because if you happen to have neuropathy from an autoimmune disease, then your symptoms aren't going to improve at all until your immune system stops attacking your nerves, and the Neurologist might be better dealing with the symptoms. If it's just post-viral, then it probably will improve eventually. It's worth trying Florinef to see if you get some relief.
My son takes florinef. This controls his dizziness, but none of his other symptoms. He was prescribed it by a cardiologist.