concerned about career shift into mental health counseling

concerned about career shift into mental health counseling I've had an intuition for a while telling me to pursue a career in counseling/therapy but I've never took it seriously due to the social anxiety I get from stuttering. I'm an extrovert at heart but due to my stuttering, instead of getting energized by being around others I get depleted. I think some of you may empathize with that. I actually love talking and connecting with people but stuttering creates a wall between myself and others. Instead of loving conversation I end up fearing and dreading it. I also find that the more I stutter the more inarticulate I become (lose train of thought, becoming anxious), so expressing myself becomes a hassle. Knowing how many people suffer in the world and feel misunderstood and alone in their suffering is what motivates me about becoming a therapist. I think it would provide so much fulfillment and meaning knowing I'm truly helping people. What I'm worried about is my patients becoming uncomfortable with my stuttering. I feel like its such a burden to the listener sometimes. Its also hard to stutter without struggling and feeling anxious. Like I wouldn't want my patient worrying about making me uncomfortable about my stutter you know? because a lot of listeners think your nervous when you stutter and get uncomfortable. A patient needs to feel comfortable, and I don't know if I can provide that. I'm also worried about never getting to a point where stuttering becomes an afterthought in a conversation. What do you think? would love some advice :)