I cried a lot when I was younger but I went through the same thought process your going through now. Everyone has their flaws. Now I care much less about it and it has meant I have done things that I thought a stutterer should never do ( I worked as a service rep over the phone for a year) and I realised most people cared less than I do. I’ve now moved onto a bigger company and have seen a head of department who has a severe stutter be one of the most respected people in the company. Be proud of who you are, and your flaws. People will always see that.