Never said you won't die. You will die a couple of times. It's takes some time to get used to the mage gameplay. It's not the same approach as a warrior who runs up to enemies and starts slashing away or sneaky bow and dagger guy who is invisible. Where you would have most trouble is between levels 15-25 where enemies switch to their slightly fancier 2 named cousins that hit hard. But that's all they do. They are not more aggressive, they are not smarter, they are exactly the same. Thing is at beginning levels the game gives you a lot of break where the enemies don't hit that hard giving you lots of room for error and making you feel comfortable. When you feel comfortable, you feel confident enough and then after blowing up a few single named bandits, draugr, wolves and spiders, here comes the cousins, the bandit marauders-chief, draugr-murderboss-deathlords, snow wolves, cave-snow bears, snow tigers and one shot you. And they will one-shot you.
So what you do is you identify those first, usually by their color or their apparel, if they have a 2h weapon or expensive arrows and you hurl a few fire-snow-lighting balls at them. Don't do much damage? This is too much for you for now. You come back when you've leveled and try again. You will see that next time you will do more damage. You may feel more confident in taking them on now. However, there is still the danger of getting killed in a few hits. That's where the fun of a mage gameplay come in (at least for me). That's where flesh spells and defense type of spells come into play. If you cast flesh spells, they will save you and you will have some room for error and take a few hits giving you enough time to turn around, get to safe distance and heal, use a potion. The first thing you want to cast when you spot an enemy (If this is too much you can always go battlemage and be a tank with spells). Or you might use fear-calm spells, the restoration ones when fighting draugr or paralize if using alteration of the sand rune spell which will give you about 30 seconds to rest before the enemy gets back up. Don't really recommend cloaks as you have to be in melee range for those to work. Except whirlwind but sometimes it works, sometimes it doesn't. If you're using shouts, then ethereal, force, sprint, ice, whirlwind are very useful "get away from me!" shouts.
Important to note is that you need to learn to manage your magicka. Don't spam the shotgun (dual cast + impact). You will run out of magicka fast spamming it. Use it for when they get too close. Rather than dual casting, use right hand, left hand, right hand, left hand combo when using destruction. You will have a higher DPS and you won't run out of magicka as fast as when you're dual casting.