Potions and especially silver flames potions are the only way to build a true BYOH barbarian.
During heroic levels you can heal using CSW potions from house kundarak and a hireling. It is super easy if you don't zerg like mad.
Just aggro a few mobs at a time and you'll be fine.
As soon as you get to lvl 14 you should be able to access to silver flame potions.
Max dodge, prr, blurry, ghostly, move smart, Max heal amp.
Pop displace for tough fights. Spell absorb, fom on gear. Worship UMD.
FOM, Deathward and fireshield are more important than saves and the DPS of a barbarian can kill stuff before they can cause you troubles.