Hi there! I stutter too and can relate to your experience. I used to stutter pretty bad when I was younger and I still do from time to time, but it has improved. There are days where when I do stutter, I feel self conscious about it and it embarrasses the hell out of me. I even brought it up to a friend and expressed how it makes me feel. But they actually don't really care or mind it. They don't notice it unless I bring it up. It's made me feel more confident in how I speak. So yes, people don't really pay attention and you just have to not think too much about it and move on. With this, I try to not think about it when I have my stutter moments.