Being new to the game and just to a new dungeon.. deaths are going to happen, its about learning from what killed you on the next pull or attempted at the boss/dungeon.

As a healer main your job has to be to stay alive and keep others alive, that means learning what attacks do and avoiding them..

a lot of attacks have different names but behave the same way.. like for example all the cyclones an most of the giant minotaur have a swing and a swipe attack.. they're usually not shown as markers and you'll have to learn how to avoid them or you will most likely die from the damage..

Its might also be a good idea to try out another class, maybe a DPS until your more comfortable with the fights. I'm not saying you should stop healing but if your having so much stress you want to quit.. maybe its time to change jobs, at least until you sub runs out.. then decide if you want to keep going.

Good luck!