Megumi is not dead in the JJK manga. The manga continues to feature him and his adventures. The story hasn't reached a point where his character is killed off.
As of the latest chapters I've read, Megumi is still alive in the manga. Usually, such major character deaths are significant plot points and would be well-publicized if they occurred.
He probably went through a range of emotions. At first, he might have been in shock, unable to believe that such a thing had happened. Then, he would likely turn to his family and friends for support while trying every possible way to find his love. He could have also offered a reward for any information leading to the safe return of his love. He would be constantly worried about the safety and well - being of his loved one.