It is possible to have a pimple appear on your lip. However, Med-Health.net reports that it is also very common to mistake a pimple for a cold sore.
Med-Health explains that a cold sore is generally a group of sore bumps around the edges of the lip. Pimples on the lip usually only appears one at a time, and they are less tender than a cold sore would be. Whereas cold sores are transmitted as a form of herpes through actions such as kissing or sharing lip balms, pimples are caused by bacteria build up. Most cases of either cold sores or pimples disappear over time, or they can be treated using home remedies or medications.