This doesn't sound like MS, but only a doctor can know for sure. If you are getting irritations that blister/ peel then you should go to doctor ASAP!
If you are going to get checked out for infections, be sure to also get tested for Lyme Disease, Bartonella (b.henselae), and possibly Rocky Mountain Spotted Fever. Lyme and Bartonella can start gradually, without an acute onset of flu like symptoms.
Some Lyme patients have described a similar rash, but some Lyme treating doctors think the rash might actually be from Bartonella, which is carried by ticks and over a dozen other insects, not to mention cats & dogs. All three of these infections can also cause neurological symptoms.
Be sure to emphasize the tingling and weakness that preceeded it, so the doctor doesn't just focus on the rash. If it were just an allergy or dermatitis, I don't think you would have experienced tingling & weakness.
Rheumatolgist or Neurologist should do.
if the rash is related with the rest and not coincidental it should be from an autoimmune disorder or an infection. secondary Syphilis for example can give rash in hands and Neuropathy.
before you go to a specialist ask your doctor to prescribe Complete Blood Count, esr, liver and renal function.
if the specialist will recognize the rash he'll know what to do in any case there are many blood tests related with your symptoms, Complements System, CPK, antibodies for some autoimmune diseases like Lupus, Scleroderma etc.
MRI brain/spine
if there's severe weakness in the arm EMG
another less common and invasive test is Lumbar Puncture.
there's a possibility that all tests will turn out negative which is good on one side but will leave you hanging on the other side.
your symptoms are not necessarily the early manifestation of a chronic disease, it could be something temporary that will resolve within months or years.