Red patches or bumps on the skin is generally caused by a rash---also known as dermatitis. There are many different types of rashes that might cause redness around the mouth, such as an allergic reaction to using new skincare products or skin conditions such as perioral dermatitis, or sebhorric dermatitis. In order to treat redness around the lips, you can make changes to your everyday routine to help reduce the appearance of the redness.
Clean the affected area with a clean washcloth, soaked in cool water. Gently pat the area dry with a towel, and do not rub it---this could increase the redness.
Eliminate any new products you might be using on the area, such as a new facial cleanser, or new make-up. If the redness happened suddenly, this is a good sign that the redness is caused by allergies to a new product. Eliminate the new products for a few days and see if the redness is relieved.
Avoid using any harsh cleansers, alcohol based lotions or skin creams that contain steroids on your face, especially near the mouth area. This will help reduce the appearance of most redness caused by rashes, such as perioral dermatitis.
Apply a layer of hydrocortisone cream to the affected area. This cream is available without a prescription and will soothe the skin and help eliminate redness.
Wash the skin around the mouth with a gentle oatmeal cleanser if you experience any irritation or redness---the oatmeal can help reduce these symptoms.
Practice yoga, or other relaxation techniques to help you reduce stress---some redness and skin irritations that can occur are made worse by increased stress. Reducing the stress in your life can help reduce the redness of a skin rash around your mouth.
If the redness persists for more than a few days, be sure to contact your doctor in order to diagnose the problem. Some skin conditions that cause the mouth to be red require prescription antibiotics.