If you go to a speech therapist in the US, look for one with the initials BCS-F after their name (e.g. Speech Therapist, CCC-SLP, BCS-F) which stands for Board Certified Specialist in Fluency Disorders. There's a push now in speech pathology to emphasize treating the cognitive and affective components of stuttering, not just the stuttering itself, and someone with board certification will absolutely have the skills to address both.