Dear Kristi, Rashes around the mouths of infants and toddlers are common especially during the wintertime when runny noses are virtually constant. Most of these rashes are caused by irritation from saliva and nasal mucous. If a pacifier is used, the saliva may be increased or trapped between the pacifier and the skin. This type of rash generally goes away with either discontinuing the pacifier or using barrier protection such as vaseline around the lips. Other rashes may be caused by eczema which tends to run in families.
Some children are allergic to certain materials such as metal causing a contact dermatitis.
This is probably unlikely from the pacifier as it is most likely made of plastic which is typically non-allergenic. Finally, an infectious rash may occur when the skin gets infected after having had sufficient break-down from irritation. This is called impetigo which requires at least a topical antibiotic ointment and may need antibiotics by mouth. Kristi, if this rash has been getting worse or not improving for three days, I suggest she see her doctor to make sure there is no infection present. In the meantime, try to limit the amount of time with the pacifier as much as possible.