Actually duele is correct, the verb duele is referring to "it". As in "it" hurts my eyes. Duelen in this sentence would change the meaning to, they hurt my eyes.
You shouldn't be giving advice in language you don't speak well, my friend, because the verb is referring to "them", the eyes. Do you say "My eyes hurts" in English? No? Well... neither do we in Spanish. We say "My eyes hurt" (Me duelen los ojos), where the verb is in plural to agree with the subject, which is in plural.
Whether you are likely to hear this from any native speaker, I won't argue against, but the natives I have spoken to wouldn't make say "duele" with "los ojos", and in proper Spanish it would be dismissed as an unacceptable mistake, whether you like it or not. I bet people prefer to learn "the correct version".