It must be very uncommon if possible at all. I think the "me" is superficial. https://books.google.com/ngrams/graph?content=my+leg+hurts%2Cmy+leg+hurts+me%2Cmy+leg+is+hurting%2Cmy+leg+is+hurting+me
I would say that "My left eye harts" and "My left eye is hurting me" are equivalent and both are definitely used . Also, it looks like the literal translation of the Czech sentence might be "Left eye hurts me," which sort of brings it closer to "My left eye is hurting me." So -- if I had a vote -- I'd vote for your answer being acceptable. But that linked frequency chart surprises me!
We really do not say it like that. It sounds as if my left eye was lying on the table and hurting on its own without affecting me. "Bolet" is always accompanied by the person afflicted by the pain (a direct object), unless we're talking in general, e.g. "Po dlouhém výletu bolí nohy." (After a long trip, legs hurt.)