Hehe, at lower levels, it's hard to be the big ol' tankaroo in Skyrim. Especially against Bandit Chiefs. I also do believe Bandit Chiefs have a generic level that does not change, and meeting one below that value makes for an extremely difficult combat. My best advice would be to stock up on potions and poisons (From stores, since you don't 'cheese' which I +1
) aswell as try to use the enviroment to your advantage. The whole hit-n-run theme seems dull for a big warrior indeed, but obstacles which can serve as a block to you while you aim your power attack may be priceless. Afterall... even the greatest warriors uses tactics from time to time.
Alternately, you could set down the difficulty. I admittedly set down my difficulty on several of my characters I've played, at the start, untill they became more power oriented or had atleast enough health to survive a coupple of hits.
Gameplaywise, as a 2h Warrior. If you're really into avoid using Alch/Ench/Smith then I applaud you. I know very few who's done the same as us. It leads to incredibly detailed tactic demanding combat, rather than the usual 'legendary armor in super enchants' godlike status it's fairly easy to reach, even on hardest. You should consider a few things, however, for this playstyle. 1: Your heavy armor won't be anywhere NEAR the quality of several upgraded light armors, so don't consider an unupgraded heavy armor much tougher than a mediocrely upgraded light armor. Also, your blade/axe/mace will rely on your playstyle and ability to utilize it. Find what weapon suits you best in combat. Personally, I loved the look of swords, but found 2h Axes was more my playstyle for the big Warrior. Not the fastest, but it seemed to compliment my power attacks well, and they're not the slowest either like maces.
All in all, just keep at it, fellow adventurer. I'll be cheering for you on the sidelines =)