Hello. I was trying to implement priority queue by myself, though I have used priority_queue from C++ STL many times. I was getting TLE for a very simple problem but when I used STL it got accepted. I believe time complexity of my priority queue for insert and pop() operation is O(log N) and overall complexity of solution is O(NlogN). please see the submission here.
Your insert method is not O(logN). Looks like O(NlogN) to me.