Thanks for that info. Barring any known blood infections (viral or bacterial), I would certainly think that the neuro is your next step. I have been reading recent studies in sports medicine dealing with muscles in athletes. The study I read looked at the serotonin levels and how that affected the muscle fatigue, but I do not think is your case.
As your brain is at the heart of your muscle controls, chances are that a neurologist will find the answers for you.
I would still encourage you to check the other boards on this site too because you never know when you will find someone who has been in the same place you find yourself.
Low thyroid levels would cause the weakness and the cold intolerance. A high thyroid level would cause the weakness but cause a heat intolerance. If your thyroid levels are fine, then you could cross this off.
Other possibilities which would fit your description could include:
Guillain-Barr syndrome, a rare nerve disorder that causes weakness in the legs, arms, and other muscles and that can progress to complete paralysis.
Myasthenia gravis, a rare, chronic disorder that causes weakness and rapid muscle fatigue. (since fatigue is not your case, this could be crossed off).
A problem with the minerals (electrolytes) found naturally in the body, such as low levels of potassium or sodium.
Lastly, a CT, I should think, should be run before you are sent to a neuro just to make sure there is not a tumor. Absent a tumor, a single nerve in your spine could also cause many of your problems. If this is the case, the neurologist should be able to assist you.