I also have a serious stutter and am pursuing Mechanical Engineering. In light of this, I started a public speaking club to try and help others who have social anxiety and/or speaking impediments. I am putting myself in the spotlight despite how much I stutter or what people say about me. Just be yourself and ignore the other people, most likely they are just jealous of good of a spot you're currently in. Good luck to you, I hope you will preserve through this! If you ever need to talk, feel free to DM me. I'm always open to conversation.