I know, im a healer and I think im a very good one, ofc im not near the best but im always on the last tier raid content.
Ofc I dps and also heal, still I dont think its stressfull, com on guys dungeons are w/e content, its impposible to get stressed on a dungeon...
If you are a new player its normal it will be harder until you get the grip to it. But if you stick to only healing you will be able to go out on every dungeons (tip for new healers I sometimes see, on big pulls on dungeons use ur stronger heals with lucid dreaming and spam it you will be fine.)
And Ill repeat myself, its a game. Relax!