Shoulder = 'ramię' (pl. 'ramiona') or 'bark' (pl. 'barki'). In my understanding, "ramiona" are more on the outside, while "barki" are closer to the neck.
Neck = 'kark' or 'szyja', but "szyja" is the whole body part where head is 'mounted' while "kark" is specifically the back of 'szyja'.
So twoje plecy are in no way "your shoulders" in Polish? That's almost identical in Russian for "your shoulders," twoi plieci.
I think I could say that my back hurts if it in fact were really the shoulders... both in English and Polish.
I can't agree on the English and Russian about that. Back hurting or shoulders hurting are distinct in English, as shoulders include the sides and front of the shoulders. In Russian, spina bolit, "back hurts," and boliat plieci are specific. The meaning of plecy must be more flexible in Polish than their Russian and English counterparts
OK, so maybe that's just my personal view, not even one about Polish. So in the comments above you can see what would be more proper.
Ja mylę "plecy" ze "shoulders". Jak się odpowiednio mówi "shoulders" po polsku?
I'd say "ramiona", which technically is plural from "ramię", which is more of an 'arm'.
To be perfectly anatomically correct, that would be "barki" (sg. "bark").
In Slovak language, both "ramená" and "plecia" mean shoulders. (or that's at least how it's used)
Is there any different Polish word for back? (we have "chrbát")
I think that chrbát is similar to „grzbiet” in Polish. Grzbiet is another way of naming back, especially in case of animals.
In Russian, pliecio/plieci [Polish spelling] are "shoulder/shoulders." Spina is one's "back."
I reported 'your backs are red' but only afterwards realised one person cant have multiple backs - please ignore that report.