Learn Polish: Co masz w oku? - What do you have in your eye?

Because it follows the preposition w (in) to show a location, it needs the Locative case. The basic neuter word oko ends with the hard consonant "k", so its Locative ending changes to -u, making it oku.

Shouldn't there be a word for "your" before "eye"?

In English, we say 'in your eye,' but Polish usually leaves out possessive pronouns like twoim (your) when talking about body parts or clothing. Since the verb is masz (you have), it is already perfectly clear whose eye we are talking about.

Is the word co (what) in a specific case here?

Yes, it is in the Accusative case because it is the direct object of the verb masz. Luckily, the word co looks exactly the same in both the basic Nominative case and the Accusative case, so its form doesn't change.

Do I need to add ty (you) to make this a question, like Co ty masz?

You do not need to. In Polish, the verb form masz already means 'you have' and questions are often made simply by changing your tone of voice. Adding ty would add strong emphasis, as if you were saying 'What do YOU have in your eye?'