This kind of thing has happened to me before too, it hurts. Talk to your friends and ask them if they can introduce you when meeting new people, there’s no shame in that. My girlfriend jumps into conversations all the time for me when she can tell I’m about to struggle on a word. It always helps me too to name the elephant in the room when I have awkward moments like this and tell the person that I stutter. Ignoring what just happened only makes it more awkward