In Doctor Strange it was shown that Eye Of Agamotto can be used to manipulate time for even a specific object (as in the case of the apple). Why didn't Dr. Strange use it to heal his hands.
Because it doesn't matter anymore to Doctor Strange.
When he gets the Eye Of Agamotto, things go fast paced and he didn't have any opportunity to do so. In the end, he accepted his role and learned his lesson. He is not going to mess with time for his selfish goals anymore. He did mess with time but only to save mankind.
Also, we don't know if the Eye of Agamotto is able to fix one body part without affecting everything else. Because time-reversing his whole body might affect his newly earned skills.
Almost as soon as Doctor Strange begins to mess with the Eye he's told that he should never touch it again, due to how dangerous it is.
Of course he does use it again, but only when the alternative is the destruction of this reality. I doubt he'd risk tearing apart reality just to heal his hands. Especially considering that he learns from the Ancient One that he can heal his hands by channeling magic through them. Why risk tearing apart reality when you can accomplish the same task through relatively trivial magic?