I would say you don't want to think of it as fixing speech. Your speech is not broken, it is just different. What you probably want to work on is your speech controlling what you do or don't do, negative feelings, shame, secondary behaviors you've developed to try to avoid stuttering. A great speech therapist can help with all of that. The unfortunate part is there are few great speech therapists who understand stuttering and know how to help. I wouldn't stop looking as I had to find a great one before I made progress. I would personally avoid ones that focus on fluency or trying to fix stuttering and look for one who talks to you about your goals and works with you on steps to get to where you want to be. Also reducing secondary behaviors will be helpful in letting you stutter more openly and slowly reduce the shame of it.