would recommend a warm soak to get the shrink out, then let it air dry. Should be good to go for hemming after that. Avoid washer and dryer. I ruined a few jeans/chinos from Gustin thinking they could make it through a cycle unharmed and I paid for it.
^ I think the coat looks sharp but I can see what you mean regarding the tightness around the shoulders. Can you fold your arms comfortably across your chest or do you feel a lot of tightness in the shoulder/back area when do this?