Dude... you have to play the original The Last of Us before playing the sequel...halfway through Last of Us 2 at the moment. holy sheeet. intense af.. i need a break and maybe something a little more light hearted for a bit.
I mean, I didn't play the sequel yet, but the first one holy sh!t! It's one of the best apocalipse stories in any medium, the ending is gut wrenching (and so is the intro btw, sh!t). I would try to play the first game if possible (for the story), you wouldn't be disappointed.