Talk to your employer about your speech. The Americans with Disabilities Act (ADA) prohibits employers from asking employees about disabilities. You have to start the conversation.
Ask your employer to help you improve your speech. That could mean time off to go to speech therapy or help paying for an electronic device.
If speech therapy is going well ask to change to a job that requires talking to more people. Talking many hours a day is essential to make therapy stick.
We’ve heard many stories from stutterers who talked to their employers about their speech and their employer said, “You’re our best employee and we want to promote you. We’ll do whatever you want to help you improve your speech.”