First of, you are welcome on this subreddit and thank you for taking the time to try and better understand stuttering and eductate yourself on how best to interact with people who stutter (pws) and about the speech disorder. As for your question. Honestly I'm not sure why your throat is tightening. Were you deeply moved by how much struggle that person was put themselves through in order to talk to you? Sometimes sometime deeply moving can elict such a response. Are you thinking that perhaps hearing them stutter somehow triggered you to stutter (have a silent block) ? Well that's not possible either because stuttering isn't known to be transferable and there aren't any scientific studies that find such a thing to be true. It's only somewhat hereditary and they've found a gene for it.