I think the first thing you need to do is consult a speech therapist. I have a speech impediment but I don't let hold me back. I don't let it define who I am. If someone wants to poke fun, let them. Does it hurt, of course, no one likes to be made fun of but I try to not let it deter me. I'm not saying it's easy and it's fucking annoying that I can't say what I want when I want, but I've been in therapy for a while and it's helping. I highly recommend the same for you. Just so you know, my job involves a lot of talking (implementation project manager for a startup software company). You've got to realize, everyone has something that holds them back and makes them want to quit, you just have to figure out if that is what defines you.