Actually that is likely her urates and urine mixed. Pus in chickens is solid and cheesy. However, I wonder if she hasn't broken an egg inside (the fluid), continues to do so, and is now infected.
First, is she of laying age? Has she missed eggs lately?
If so, then the first thing I would do would be to get gloves, a baster or syringe without a needle, some cool water, some olive oil, and put her in the tub. Put on the gloves and oil the fingers of your right hand. You will insert the index finger into the upper part of her vent, gently, not pushing if you feel resistance. Please use a helper to very gently but firmly hold her. Look for a wound opening. (I don't think you'll find one but it needs to be ruled out.)
Feel inside the vent for any masses, egg shells broken, eggs, etc. Use your other hand to hold the abdomen and very very delicately palpate it. Feel the skin between the outside and the inside under the vent and try to locate the fluid. Is it in the meat? Or is it in the vent?
You will want to fill the baster with cool (not cold, not warm) water and flush out her cloaca gently. Look at what comes out - does it look at all like yolk to you? Or more of the white? Flush all of that out. The cool will cool inflamed tissues. The flush will clean stuff out that might otherwise continue to infect her.
If she's a young bird, please say so and I wouldn't recommend the above.
As for antibiotics, the ones you would give with water and feed aren't the right ones. The 'cillins are correct for this - a wound or internal peritonitis. Injectable penicillin is sold at the feed store in their refrigerator. Penicillin G procaine, or regular plain Penicillin are good choices. THey require a 3 cc syringe and an 18 gauge (any length) needle. Most stores sell 3 cc syringes with 25 gauge needles attached for dog/cat shots. You can unscrew the needle and replace it with the screw-on 18 gauge needle. Penicillin is thick and the particles in it are large so you need the bigger size needle, to shake it absolutely thoroughly before using, and for the shot to come to room temperature before giving the shot. (Store the vial in the fridge.) PM for dosage and how to give the shot.
You will want to keep the area well cleaned off and dry. If you see broken skin, cleanse it with nolvasan and water, or a little iodine in water (made into a light tea-colored solution). Pat dry, and dress any sores with neosporin ointment. You can even use a little baby powder or cornstarch on the area to dry up the skin a bit and easy her irritation.
In the mean time, please tell us what she's eating, etc? Everything including grit, granite, oyster shells, treats. Where is she kept (coop/run, free range, etc). Please tell us her laying history in detail.
To help her heal, giving her yogurt (plain - 1 tablespoon) daily and some vitamins'/minerals in the water will help til we get a better idea of what this is. The yogurt will help if this is a yeast infection (very possible) or a bacterial digestive issue as the yogurt contains living bacteria of the same good type that are inside the bird. Those good bacteria help prevent illness and help heal if there is one.
I'm waiting for your reply before I say more.
