If you intend to keep this hen, it's time to manage her properly. Chickens are domestic animals, and unlike cats and dogs, they will not revert to the wild. With the exception of a few breeds, they require the kind of care all farm animals require. Fortunately, it doesn't take much to get a chicken to trust you if you're willing to spend a bit of time each day for a few days.
First of all, please collect all of the eggs you see. Do not be intimidated. She may peck your hand, but it doesn't hurt that much. Use gloves if you need to. The bad smell equals bacteria, and you need to get rid of all sources of it. After you collect the eggs and dispose of them, clean out all soiled material in the nest boxes where she's been sitting. Replace with fresh.
As for the hen, you do need to treat her with more calcium. The smelly discharge is typical of material that needs to be expelled from the oviduct. The calcium encourages the contractions necessary for this. The only trouble with Tums is the sugar and flavoring in it. Go ahead and give her one, and then next time you get to Walmart pick up some of this.
View attachment 3776377To make friends with a chicken, start by offering a treat off your hand. Gradually move on to touching and stroking the breast or front of the neck. When you offer treats, make her come closer each time. Soon you can train her to come to you if you use an audible cue each time. Chickens learn quickly to come when they associate a particular sound with a treat. Once she is coming to you, pick her up and hold her often. Some chickens learn to crave this closeness with a human, and they rival dogs and cats in liking affection.