Should I be seeing a speech therapist or a actual psychologist for my stutter?

Should I be seeing a speech therapist or a actual psychologist for my stutter? I don’t stutter when I’m alone as much but when I speak to people, my stutter is definitely there. I find hard to talk basically. It’s also the fear of opening my mouth and talking and fear of the stutter. It’s also social anxiety. Maybe I should try seeing both a speech therapist and psychologist? But if I can only see one, which one is more beneficial in my case?