Closed mouths that are red when squeezed are recommended to be treated with medication and physical therapy.
Closed mouths are closed pimples, a type of acne, and may become more inflamed if squeezed. It can be treated with topical medication, which is usually based on antibiotic creams such as fusidic acid cream. After the inflammation subsides, closed acne can be removed with topical retinoids such as adapalene gel and retinoic acid cream, which have the effect of dissolving acne, and the drugs are irritating and need to be built up to be tolerated. Normally, you should avoid squeezing the acne, so as not to leave behind discoloration and scarring.
All of the above medications are recommended to be taken under the guidance of a doctor and should not be used on their own.