You are probably experiencing a condition known as dermatitis (an inflammation that usually involves swollen, reddened and itchy skin).
Sometimes, it is called ezcema.
There are different forms of dermatitis,like irritant and allergy contact dermatitis, but, when the itching is very prominent, the affected area is largely swollen and blisters are more common, the diagnosis is more suggestive for an allergic contact dermatitis.
Possible factors for triggering this condition are lip balms, lipstick, toothpaste, mouthwash, bubble gum (ie, rosin, cinnamates), nickel in musical instrument mouthpiece, rubber in snorkeling mouthpiece, cane reed in a clarinet, food (eg, mango skin).
The ring around the mouth is an inflammation, too, and is called perioral dermatitis.
The same triggers for lip dermatitis, may triggered the perioral dermatitis, too.
This condition is harmless, but, the ring will be present for months or years if it isn't treated.
Usually, an antibiotic therapy is prescribed for a period of 12 weeks.
Avoid make up foundation, since it is considered a strong provoking factor for perioral dermatitis.
Best wishes!