What are you using for a weapon/sheild? A shield is really important, rather than just getting pounded by draugr.

When you get a bit of iron, make the iron banded shield, but just starting out in the swamps, I like the bronze buckler.

To use that effectively you should learn how to parry. It's not hard, you just need to get the timing down and block just before they swing. You might want to practice with skeletons or something similar.

If you can parry the draugr, you stagger it, and then it's not hard to kill with any of a number of weapons.