What kind of doctor deals with the arm?

Tingling sensations of the arm does not really require a visit to a specialist, orthopedist.. more specifically. You can simply go to your nearby hospital and get an MRI done. They will decide if a specialist is necessary or not.

Answer

Start with your primary care doctor if you aren't already a patient of a specialist. You should be able to answer questions of when the tingling occurs, whether it is continuous, how many days it has been going on and any other feelings (like dizziness or pain elsewhere) you have at the same time. Otherwise, you can spend a lot of money on an MRI and find out it is nothing.