If you feel like you stutter, you probably have one. I don't see why anyone would fake it. My dad also doesn't believe anxiety or depression are real. He kind lf just ignores thag I stutter. Most of my family does actually. All I heard growing up was "why are you so shy?" "speak up more" "speak slower". That aside, you're describing a stutter, but if you're still doubtful, see a speech pathologist.