She's having a reproductive crisis. It's called prolapse as
@Eggcessive mentions. It happens sometimes when an egg gets stuck inside and/or breaks. It may now be irritating and inflaming her reproductive tract.
There are some things you should do for her if you want her to recover and be able to lay eggs again. First, I put such a hen on an oral antibiotic immediately. Penicillin or amoxicillin 250 mg per day for ten days.
Next, I give a tablet of calcium such as human women take, one per day until her crisis resolves.
She should be moved to an infirmary crate where she will be safe from the other chickens pecking at her prolapse and injuring her so badly she may need to be put down.
Gather witch hazel, Preparation H or hydrocortisone cream. After soaking your hen in warm Epsom salt water for about fifteen minutes, dry her and wet a cloth with the witch hazel. Use this wet cloth to push the prolapse back inside. Then smooth on some cortisone cream or Prep H to help shrink the tissue.
You need to monitor her poop and watch for egg shell, egg yolk, and membrane to be expelled. Until it's all pushed out of her, her prolapse probably will not remain inside. She may have a steady dribble of clear liquid and that will tell you she's still trying to push out the egg remains. The yellow you saw around the prolapse may be evidence there's still egg material still inside.
Check on her frequently. Use the witch hazel wet cloth to push the prolapse back inside. Be sure to give her the calcium since that will strengthen her contractions to clear out the foreign material. The antibiotic will safeguard against infection caused by bacteria taking advantage of the inflamed tissue caused by the egg mishap.
Be patient. Keep pushing the prolapse back inside. Keep it moist with the cream.
Do not let it dry out. And be patient. It can take a week or more to clear this up and have the prolapse stay in. My last patient took ten days. She was a ten-year old hen with a broken egg inside. She made a full recovery.
