I've only really played as a mage who died frequently and I decided to try as a warrior who dies even more frequently. My biggest problem is mages and dragons. Any advice?

Atronach stone and jewelry with resist magic or element enchantments. Potions of resist magic and lord stone are options too.

Close the distance quickly and smash, smash, smash. At least for mages. If you have unrelenting force use it to disrupt the mage. What level is your warrior?

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or for dragons, put a couple points in staminda, and bash/power attack frequently. The more he stutters, the less damage you take.

What is the difficulty setting. You can try lowering the settings.

Are you using any mods?

With my warriors I go for the Lord Stone and put all my points into Health.

use a shield and get the elemental shield perk for reduced damage vs mages and dragons.

normally i go for a kill to live style of combat with absorb health on my swords and health restoration on my armor.

glass cannons sure are fun.