Emily, with your symptoms I would expect an abnormal EMG/NCS. Once you have numbness in your feet and lower legs it will probably show up on a skin biopsy as well.
Some of my symptoms were gradual and ignored as just being clumsy, lazy, etc. I had a dysfunctional family situation which complicated things, it was in no one's interest to diagnose me with a genetic disease since I was the product of an adulterous relationship.
I did develop hand and arm weakness very suddenly about 8 or 9 years ago. I couldn't hold plates either, and couldn't take wash out of the washer, carry groceries, etc. it was diagnosed after an EMG as carpal tunnel, but this was later found to be incorrect as it was a flare up of the CMT. It is usually gradual but there can be exceptions. Everyone is very different with this disease as Kitt said and anything you read will probably make unwarranted generalizations. It used to be thought that pain was uncommon with CMT. This has been disproved and my pain is quite severe, but many sites repeat outdated information, even the Mayo site has lots of inaccuracies.
Physical therapy gave me back a lot of strength in my hands at that time. Later I lost range of motion in one arm such that I couldn't dress myself, again therapy helped. Last year I sprained my ankle and physical therapy allowed me to continue driving a little, I have virtually no motion in my ankles now, but can drive for about five minutes which takes me to the doctor, dentist, and food store.
The doctor should be very interested in your family history, if they aren't diabetic this must have a hereditary component. Your symptoms are perfectly consistent and should be taken seriously.
It took my podiatrist to actually get the ball rolling. He refused to treat me again after I went to him with a foot infection ( he did treat the infection ) until I saw a neurologist. He said I had the worst neuropathy he had ever seen and that bilateral neuropathy in both hands and legs wasn't simply carpal tunnel, especially with my other symptoms - high arches, tight Achilles' tendons, poor gait and balance, etc.. He thought that my height (6'2") made it all worse since it is length dependent.
Another thing that caused a sudden worsening of my symptoms was Tricor, a medication I was given for extremely high tryglerides. It quickly exacerbated my balance issues to the point that I could no longer walk without falling. I improved as soon as I stopped it on my neurologist's hint.
They should try to find out if there is a treatable cause for your symptoms, but CMT is progressive and incurable. My neurologists both said "good-bye and good luck." Chronic disease makes doctors uncomfortable. It is a relief to have a diagnosis and the progression is usually slow, but it is a big thing to accept, especially at your age. I hope they can help you.
I was extremely flexible when I was younger, except that the muscles in back of my legs were always tight, and so is my one son, although less so than he used to be. I have read of other CMTers with this trait.