I say do it because It can only do you good dude. I have more of a mental stutter as well and don’t stutter around family or friends as much but rather in front of strangers set up by social anxiety. The remedy I would recommend for this is: yes see a speech therapist and doctor about trauma if you haven’t already and work on meditating and building self confidence in your self whether it be through exercising, school, work, etc. There have been times where I’d say the sentence a hundred times out loud in the car and then when I have to say it to the person I flunk. It’s all in your head and it’s a muscle contraction block that you need to learn how to manage. I didn’t have head trauma but I didn’t have a stutter until I graduated high school because of social anxiety, insecurities, and depression that brought back the same stutter I had when I was 9. Point is, if it’s caused by anxiety there is definitely a way to work on it from my experience.