This is a tricky one. Going by bare definitions according to the Cambridge Advanced Learner's Dictionary, improve means
to (cause something to) get better
while pain means
a feeling of physical suffering caused by injury or illness
Taken literally, if you described the suffering itself getting better, rather than the feeling associated with it, that would mean the actual pain is getting worse because from the perspective of the pain, hurting you more is a good thing (I didn't foresee myself anthropomorphising pain today, but there you go).
However, most people would interpret "my pain has improved" as meaning that you're feeling less pain than you were, as very few people outside the realm of sociopaths would consider you feeling more pain as an improvement.
The bottom line is that it's fine to use this construction, but only because nobody is cruel enough to apply the literal meaning of the words. :P