This is, unfortunately, a normal experience. I have a fairly mild stutter, and even I had an interview where I shook someone’s hand and completely blocked on their name (something that never happened before or since). I sat there and held her hand for around a minute (felt like a lifetime) as I struggled to say ‘you must be ____.’ I couldn’t share a single story without stuttering, and I left knowing it was a mess. The recruiter called me afterwards to ask how it went and thought I was being too hard on myself. I’m usually very confident in interviews (fake it until I make it). This experience will pass, they will forget about you five seconds after you leave, and the right organization will recognize your skills aren’t dependent on your speech. You can also try using disclosure statements to help get ahead of it. I personally have my involvements with the National Stuttering Association on my resume.