Stuttering and a variety of speech problems may be helped with acupuncture but you would need to see someone locally to look over your case (i.e. what is behind your stuttering) and then after a few treatments you should get an idea of whether or not acupuncture can help you. There are physical, psychological, and neurological contributors to stuttering and only someone who performs a proper TCM intake and diagnosis will be able to recommend whether or not acupuncture is a viable treatment option for you.
I wouldn't necessarily look for someone with experience in stuttering as it isn't commonly seen by many acupuncturists. Anyone that has some experience with stroke rehabilitation and/or neurological conditions (i.e. most acupuncturists) will be fine.
Just for completeness sake, I will offer some of the points that we most often use. They probably won't mean much to you but will mean something to other acupuncturists who read this forum.
We use both deep tuina and acupuncture (as appropriate and adding tcm points related to an overall tcm diagnosis):
<li>Huatuo of C2 on the left side</li>
<li>GB 13 on the left side</li>
<li>SI 16 </li>