I'm the exact same size. I'm guessing you need about a 19.25-19.75" chest in your tshirts.
Michael J krell fits that need.
Also, urban outfitters bdg 50/50 polycotton shirts are soft and the medium is about a 19.5-19.75" chest and fits slim. Like cldpsu said, the do sometimes develop neck holes as i have 2 of them and 1 of shirts has it. However, i really don't care that much. It's not noticeable at all to the eye or feel. I can only tell if i stick my finger there.
American Apparel shirts after you wash them fit in between small and medium too because those shirts shrink a bunch. The medium is normally a bit too big but the wash makes it shrink half a size. The small is normally too tight though, especially after the wash. The AA 50/50 shirts however fit slightly different and i seem to wear a small in those.
I've also found gap athletic fit size small to fit like a slim medium as well and the length is fine and i'm 6'- 6'1".
Most designer brands like dior homme and some other will have their mediums fit slim to work well with that in between size.
With that sizing i find that i'm pretty much always a size small in mall brands and a small in outerwear and jackets. Maybe i have narrow shoulders or something, but even in brands that i'm a medium in tshirts, i still need a small in jackets or button up shirts. H&M is like that for me. I'm a medium in their tshirts, but i have a westerny button down shirt where a small is better.