does being childish mean I'm immature?

I watch cartoons, get sully when I don't get my way, loves spending time with kids e.c.t count as being immature?
I'm very serious with my studies, and my friends come to me with their problems because the consider me the mature one e.c.t.
But my ex's last words were "you're childish for hardly considering my feelings near the end of our relationship" and I called him immature.. as he cheated on me.: