I assume Tommen killed himself because he loved his wife and he knew that she was dead because he was a weak king who wasn't able to control anyone, including his mother. He feels like a failure as a king and decides that the only way to be back with his wife is to kill himself.

The show writers have described Tommen's death as the thing that causes Cersei to turn into the mad queen. She doesn't cry for Tommen because she no longer feels love, only hate. Tommen was her last line to being a normal loving mother. With that gone, she will be cold and ruthless from now on.

I wanted to give you an update from a further 3 years in the future that the show is doing better than ever.