That is very normal. It's because you feel that the spotlight is completely on you, as if you are under a magnifying glass. Many people who stutter feel that everyone focuses on their every word and sound, which is actually not true. Only you do. Other people tend to focus mostly on your message, on what you want to say rather than on how you say it and cut you some slack if you have a bit of the stutter. Unfortunately, if you get stressed out, your stutter gets worse and then you feel even more stresse - a vicious cycle. There are some really helpful CBT (cognitive behavioural therapy) techniques to help cut through the habit of over analysing your speech and giving yourself a break.