It sounds like you probably have something called Fordyce spots. These are small, yellow or white bumps that are painless and are found along the border of the mouth within the colored portion of the tissue of the lip. These Fordyce spots are actually normal oil glands which, for reasons of individual variation in pigmentation and skin thickness, are more visible. They should generally be left alone, as picking at them may result in scarring, inflammation, or infection and will not remove them permanently.
Oral herpes lesions, which are another common cause of sores on the lips, generally look quite different. Herpes lesions generally begin at the corners of the mouth (although they can appear anywhere) and the begin as small blisters that then rupture, ulcerated, and crust over before healing slowly. Herpes lesions tend to be painful.
Occasionally trauma to the lips (such as from frequent biting) can lead to small areas of healing tissue which can appear white against the background of the lip color.
Acne is common around the mouth, both whiteheads and blackhead, but it is unlikely to occur within the colored portion of the lip border, which is where you are noticing these bumps.
If you have concerns, your primary care doctor
should be able to take a look at these spots and determine if they need treatment.