Hi and welcome,
What you've described experiencing is actually what neurological conditions like MS don't cause, which is basically because of the way brain and or spinal cord lesions present and continue to develop over many years.
The symptoms they cause develop in specific locations during a relapse and then they remitt, until months or years later when the MSer has another relapse, the symptoms come back in the same location as before, as well as other locations with any new lesions that developed.....theres more too it but thats the nuts and bolts of why conditions like MS don't cause symptoms to move locations, rapidly develop, only last seconds etc etc...
It is possibly health anxiety related IF you are dealing with a high level of anxiety, its more likely along those lines if you dont seem to have symptoms during the day when your busy and distracted, or you experience symptoms when your thoughts are spinning....
Alternative causes of sensations in peripheral limbs that move around are numerous, to be honest its hard to guess, it could be many different types of things eg bad posture, autoimmune diseases like Hypo Thyroidism, Lupus, Diabetes, vitamin deficientcy, menapause etc
I would speak to your GP about needing help and support to deal with your current anxiety and a general check up to see if there is a medical explanation for these odd sensations you've been experiencing on and off for the last few months, and hopefully you'll get pointed in the right direction.
Hope that helps......JJ