Learn Polish: Kolano mnie boli po meczu. - My knee hurts after the match.

In Polish, you don't usually say "my knee hurts." Instead, the structure is "the knee hurts me." The body part (kolano) is the subject doing the action, and mnie (me) is the object receiving the pain.

Does the verb boli change depending on who is feeling the pain?

No, the verb matches the body part that is hurting, not the person. Since kolano is singular (it), we use boli. If multiple things hurt, like both knees, you would use the plural form bolą (for example, kolana mnie bolą). To change who feels the pain, you just change the pronoun, like jego boli kolano (his knee hurts).

Is it also correct to say Boli mnie kolano?

Yes, Polish word order is very flexible and boli mnie kolano is actually a very common way to say this. Putting kolano at the start of the sentence just places a little more focus on the knee itself, but the meaning is exactly the same.

Why does mecz change to meczu at the end of the sentence?

The preposition po (when it means "after") makes the following noun take the Locative case. For many short, masculine inanimate nouns like mecz, the Locative ending is -u, giving us po meczu.