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!
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
In this case, Czech requires a (possessive?) adverb and English doesn't but English requires a (possessive?) adjective but Czech doesn't. Therefore: Bolí mě levé oko = My left eye hurts. Correct!?