A psychiatrist might have an off label practice of prescribing drugs for a stutter, but it will be based entirely in anecdotes with his/her patients, not systematic evidence of a therapeutic effect of drugs. Counseling could help with anxiety ( emotions like you say) but for most people that is not the cause of a stutter. Keep in mind to to be a speech therapist (in most USA states) all you need is a degree from an accredited program and continuing Ed, but the field is broad enough that you could be licensed and know very little about effective treatments. and of course grad programs vary in rigor. I would agree about barking up the wrong tree. And find a therapist with specialization, not just someone setting up a shop with “speech therapist for hire”