I've found it almost impossible in the swamps to NOT get poisoned even using the gold hemmed outfit. The swamp is really one of the more annoying levels and being a chaos servant without the lordvessel I have to journey through that place quite a bit.
Find your next island of non-poisoned ground, and then do a run and jump towards it. That will reduce the time you are in the muck by a little bit and might make the difference in quite a few cases.
You can run around with the Gargoyle Tail and that would help, and you can buy a anti-poison ring before blighttown too. I haven't dried the rusted iron ring there, but that should be available before blighttown too to help you move through it faster.
I just ran out of purple moss, and tried the rusted iron ring. Works great! Just have a destination in mind before you step in the muck, and wait for your poison meter to drop before setting off for the next one.
Rusted Iron Ring and poison resistance gear (Antiquated, Shadow, Poisonbite Ring later Gold-Hemmed) are your best bets, but even then you get poisoned if you aren't waiting around on the patches of land forever. Also, some items are so far removed that you'll likely get poisoned even with an empty bar when retrieving them.
You can't make an omelette without crushing dozens of eggs beneath your steel boot and then publicly disemboweling the chickens that laid them as a warning.
If you backtrack up to the depths, find the butcher's room and go through the shortcut behind him, you'll drop onto the top ledge of the "rat boss" room. You can kill the boss with ranged and never have to melee it this way. Anyway, run around to the other side of the ledge without dropping down, there's a spider shield to help with poison resistance.
As others have said, there's also a poison ring and the rusted iron ring available. I had a big supply of moss from the forest and I only had the shield at the time, worked for me.