A mage can sling spells, and a rogue can shoot arrows, but a warrior (like myself) who is melee-focused must defend until the dragon lands on the ground and bash away at it.

I was wondering, if I don't want to use archery, what are some tips for fighting dragons better? I have yet to try enchanting my shield and armor to reduce fire damage. And I'm a Nord, so I got good frost reduction from the ice dragons. Is their anyway possible to completely block all incoming fire from a dragon? I always liked the idea of hiding behind my shield to defend against a dragon's fiery breath, but it looks kind of dumb when I catch on fire in the process of it.

You should get the Shield Spellbreaker, it helps alot against dragons breath, and all other magic.

Get Dragonrend as quickly as possible.

pretty much this, or spellbreaker, two perfectly viable options for your warrior, and if that doesnt do it...throw a sweetroll at it