Draugr Elite have a Slash attack that can do 58 damage. The max block on a Bronze buckler is 24 So blocking with a Bronze Buckler will still let through about 34 damage Which wit fully upgraded bronze armor would still mean you'd take about 8-9 hit points. (That is likely not accurate... I didn't actually go through and do the math based on the code I did some guesstimation) Basically you need the Iron banded shield or better. Though Even then 1 Star Draugr can mess you up for a while.

When I start doing the swamps I take Stagbreaker. Before I clear the muck to a room I usually use the AOE impact of it to clear as many mobs as I can. (and if I'm lucky any spawners) I also don't go in without the best food I can get and poison resist potions.