0k, the swamp is a real step up in difficulty from the black forest. I'll tell you how I do it and you can take from that what you'd like.

Deer, rasberries and blue berries really aren't your best bet here. The first move I make in the black forest is to get carrot food going. Starting out in the swamp, I try to be eating carrot soup, Dear pie, Minced meat substituting jerky for working time. That will add quite a bit of stamina and health.

You should switch from a sword to a bronze mace. A lot of the mobs in the swamp are weak to blunt.

The most valuable item in the swamp isn't iron, it is turnip seeds. Look for those little yellow plants like they are gold. The turnip food is fine but the upgraded cauldron (you need 3 turnips to do this) gets you sausages. Plentiful and powerful that really changes the nutrition game for your character.

You'll be at your weakest when you first enter the swamp while you are still essentially relying on bronze. So only go in during the day. Make sure you go into the swamp from another biome and work your way in. Keep your avenues of retreat always open and only go into the swamp at first when you need to and can gain from going in. Be skittish. Run from anything you can't easily beat. Use that hoe to transform your first swamp into a big muddy field and you'll be able to run from anything you can't beat.

You want to find a sunken crypt close to the border of your swamp. Go in with poison resistance in place, get into an accessable crypt, pull out your first load of iron and start upgrading your kit. I upgrade my mace first, then armor, then bow, then pick and finally axe. You might want to upgrade a different path but think it through.

Then the swamp gets a lot easier. I usually enter the swamp with my armor class at roughly 30. Pretty quickly, it goes to 50 with a root mask and that makes those draugs not as bad. At first run from Draugs with stars or anything elite, by the time you are eating turnips and sausage with iron armor and weapons, you can start fighting them.

So, get better food, start slow and work your way in, run from anything you can't beat easily and, as you improve your kit with iron, you can do more. Good luck!