Post-Elder is when the tutorial really ends. Learn about meads, find the better ingredients, take your rested bonus seriously, dock your boat at a safer biome (if you can), plan out your portals etc. You could easily neglect many of those aspects and get by at a sane rate earlier, but in the swamps they will all do their own big part in shaving off hours of time where you would be dying, recovering or taking everything you do even more cautiously.

Also spamming a hoe to level the ground in front of you as you move around the swamp has a very good chance of saving you later. Not only does lifting the ground above water this way obstruct the movement of leeches, it also means that retracing your steps backwards will always lead to a solid escape path where you don't have to worry about wading, swimming or jumping over deeper water. Do a little bit of crisscrossing as you explore and your paths will link up in a way that will enable you to navigate around that swamp almost as efficiently as earlier biomes.

If you got that many draugr wandering around there is probably a spawner. Play it safe when you are using last biomes gear and just shoot those things out.

Speaking of last biomes gear I would personally recommend swapping to the troll set for faster movement with only a minor defence penalty. It is by no means a requirement, but on top of the movement speed penalties from wearing the bronze set you are now facing a constant stamina regeneration debuff from the rain, and together they are likely contributing reasons as to why the draugr are keeping up with you and overwhelming you. If outrunning is still difficult and you aren't capable of a good block, better movement will help you conserve the stamina you need for rolling and everything else that stamina is used for.

Seriously enemies move in all sorts of ways in the swamps. They charge, they swim along the water-edges, they bounce, they hover, or they snipe you from where they stand. Most of them are not movement-impaired by the same minimum depth of water that it takes to slow you down. Optimizing your ability to manoeuvre until you get to iron gear is a solid play.