Learn Polish: Ramię mnie boli dzisiaj.

In Polish, you usually don't need to use possessive words like moje (my) with body parts if it is obvious who they belong to. Saying mnie (me) already makes it perfectly clear that it is your arm hurting.

Why does the sentence use mnie (me) instead of mi (to me)?

The verb boleć (to hurt) requires the accusative case for the person feeling the pain. Mnie is the accusative form of ja (I). English speakers often want to use the dative mi because they think "it hurts to me", but Polish strictly uses the accusative here.

Ramię ends in an -ę. Does that make it a feminine noun?

No, ramię is a neuter noun. A small but important group of neuter nouns ends in -ę, including common words you might already know like imię (name) and zwierzę (animal).

Can I change the word order and say Dzisiaj boli mnie ramię instead?

Absolutely! Polish word order is very flexible. Dzisiaj boli mnie ramię is actually the most common and natural way to say this. The order in our sentence (Ramię mnie boli dzisiaj) is also correct but puts a little more focus on the arm itself.