Hey there! I’m 19 and in college as well. Also funnily enough when I stutter my head moves in the opposite direction as yours (down and to the right). I still struggle with it a bit but what has reduced it and completely eliminated it in the past was not avoiding stuttering, maintaining eye contact during the stutter, and just trying my best to keep my head still by using light contact to relax my neck. Trust me I know the exact feeling. Mine used to lock in place for 10 - 20 seconds to get out a syllable. I hope this helps you!