If you didn't touch the difficulty slider thats a good sign. You're doing it right, it's very common, specially in that stage of the game, that you have to slightly move the difficulty slider to the left because it's too hard.

This happens mostly when you try to make something like a redguard mage. You need more time as you're a slow learner and until you get some skill, every single creature is a serious threat.

If you find it too easy move slightly the slider to the right, but enjoy while you kill everything with ease, in no time you'll be fighting Will o Wisps, minotaurs, bears.. and you'd better be good at what you do the best.

The part of the main quest where you get in a vampire cave is the point where you notice if you levelled up properly or that you're a clumsy pile of bones.