Have multiple sclerosis. can constant movement makes body tingle and numb?

Yes!: Numbness and tingling is very common symptom of ms, also movement like tremors or other movement can be symptoms--some sensory symptom make you move--so it is unclear which come first.

Yes: There is something called uhthoff's phenomenon. This is when the body temperature goes up, even slightly, and one can notice their symptoms or more pronounced symptoms. Think of it as the message short circuiting do to heat. Once you cool down, the symptoms improve. I deal with this with my ms.

Possible: Especially if you have Lhermitte's phenomenon due to involvement of cervical spinal cord in posterior columns.