Hi! Speech Path here!
How old is your son? Is there anyone else in the family that stutters? Did he go through a recent big change (new school, new baby, moved homes)? You may want to ask your pediatrician for a referral for a speech evaluation. Depending on his age, speech may not be a bad idea. Sometimes when more demands are placed upon a child, his capabilities for fluent speech decrease. Extraneous movements could be from stuttering but also from a tic disorder. So you'd want someone to rule out the possibilities. Speech therapy can help in more ways think you would think, and would be of no cost if he is in public schools.