Can a stutter be classified as Tourette’s?

Can a stutter be classified as Tourette’s? Gone through years of therapies for my speech (among other things) which have all proved ineffective but seeing as it’s the only treatment for stuttering, I’m kinda stuck. I’ve used all kinds of drugs trying to help my stutter then I took drugs just to help me cope with the anxiety and depression that got worse as I got older. Benzos and near intoxicating dosages of anxiety relieving drugs are all that have been useful but my doctors refuse to stick with anything “addictive.” So I’ve tried everything and nothing I can use long term has helped. But there are treatments for Tourette’s/tic disorders like muscle relaxants, effective anxiety meds, and multiple other classes of drugs. My facial tics that come with the stutter have gotten ridiculously out of control which got me thinking that maybe it could be a form of Tourette’s? Would a doctor consider treating it as Tourette’s? Especially since I’ve gone through every line of treatment for anxiety and depression several times now