Alchemy is your answer. You don't even have to invest in the alchemy tree too much to be able to make decent potions. Just get some alchemy increasing gear, and put a few points in the perk tree, and you're set. Find ingredients that have the restore health property. As a bonus, you can even make poisons to make your melee attacks more deadly. --- This here's ma signature!
Don't go alchemy. Warriors need stamina as well so invest in Respite and Regeneration on the Restoration perk and pick up fast healing. Your golden then. --- "Nothing amazing happens here. Everything is ordinary"