How do I handle emotionally demanding acting roles?

You can act well now, and it is the emotionally demanding roles that show you where you still end. That is not failure. It is the honest edge of the craft, the place where technique runs out and you have to actually go somewhere real inside yourself. Every serious actor meets that edge. These roles expose your limits because they ask you to touch feeling you would rather keep at a distance. The block is usually not skill; it is self-protection. Part of you guards the door to the very emotion the scene needs. That guarding is human, and it is also the thing to gently work with. Rather than forcing the big feeling on stage, do the quieter work off it. Find the small, true memory or image that opens the door for you, and rehearse walking through it safely, with support if the role is heavy. And build a way to come back to yourself after. Depth in the work should not cost you your own ground.