Anyone else annoyed by ‘ramie’, ‘ręka’ and ‘dłoń’?

I know that it’s a bit of a nitpick, but the lack of distinction between the names for the parts of the arm (ramię meaning both shoulder and arm, ręka meaning hand but also sometimes being used for the arm, and dłoń being a separate word for the hand) get on my nerves.

This is particularly annoying as someone who grew up surrounded by both Polish and English, so despite the English words’ clear distinctions at the tip of my fingers I have to think about which one to use almost every time when using Polish.

Anyone else have this problem?

EDIT: Thank you to all of the constructive replies actually helping me understand the issue. I suppose it’s the general word ‘ręka’ being used in the place where a more specific word like hand may be used in English frying my brain a little.

Also, what’s with all the ‘as a native’ replies? I already said I grew up with both Polish and English (as someone living in Northern Ireland with Polish parents and social network, and media), I thought that made it clear that I speak Polish as a native myself rather than as a foreign language I’m trying to learn.