Is stuttering and twitching associated or do I have a bigger issue?

Is stuttering and twitching associated or do I have a bigger issue? I am a heavy stutterer. Have been since childhood. Seen a therapist in school but that stopped after I graduated high school. I can’t stomach $80-$120 an hour for therapy. But for the life of me I can’t figure this out. Whenever I get stuck on a certain phrase or word my head and shoulders just start to twitch in all directions. And I can’t control it. Just recently I had a job interview and this happened halfway through. They asked me to leave and seek professional help. Idc about what people think tbh. I got used to this already. But I am curious as to where this twitch comes from and if I have a bigger issue at hand.