Yellow stools are the sign of unadequate bile flow, due to liver congestion, stones and/or parasites.
Does the red ring appear soon after you take an antifungal, like coconut oil, raw garlic, turmeric...? It would help to know.
Sometimes symptoms can worsen soon after a coffee enema, because even if it helps cleansing the blood, it produces a release of toxic bile from the liver to the small intestine. Take 1 Tbsp of activated charcoal 20 minutes before the coffee enema and see if the same thing occurs.
Regarding pure water enemas, I experienced two things: sometimes a huge relief from all symptoms soon after, but sometimes the opposite. I believe the second thing is due to the fact that toxins are being expelled, therefore allowing the body to fight better pathogens, leading to die off.

I found that the water PH used for enemas can have a different effect from one to another. The water should ideally be slightly on the acidic side.

Great advice by Kcirla. I'm always intrigued when a patient tells me they develop something after they have relocated somewhere else. You say the red ring came - after you went to NY. Could be a diet change, eating or drinking different foods? Could there be new stresses involved? A bit of detective work is a good thing when a new condition develops. Think carefully about this.
A red ring around the mouth could also be an allergy, I've seen this many times when a patient started to eat a new food, especially a fruit or vegetable, they have not consumed before. Classic food here is a mango or a pineapple.
The stool color indicates liver issues for sure. Yes, charcoal is a good one. But so is St Mary's thistle. A good formula for yellow/green stool is Swedish Bitters, take one teaspoon three times daily before foods in a little water. A nice warm castor oil pack over the liver will help as well. Have you ever had this red ring before?

Do Hunzas, Okinawians, people who live longer do enemas, fasting or other shitty stuff ??

Do what they do and you will heal cancer, candida, and prevent some serious disease like MS. Balance your diet with Hunza/Okinawa food.

The enema is doing it's job of removing the candida fungus from your system. That is why your stools are always green or yellow instead of brown. As far as the red ring developing around your mouth. I don't know, maybe it is an allergic reaction to the enemas. I suggest drinking a lot of water and the more the enema cleanses your body the less funny colors you'll see in your stool. http://yeasthomemedicine.com/

Possibly gall bladder related. Bile is possibly causing both symptoms.

Make sure your sodium intake is adequate (and water)
Add magnesium and zinc to your diet

Also would be good to start on liposomal vit c.

You can make it yourself very cheaply.
You can also add the other vitamins into the liposomal solution