The answer to this question depends on exactly where this growth is. As you are probably aware, just outside the eye is an unusual location for pimples, especially a recurring one. The best type of physician for you to see about this problem is a primary care physician
such as a family doctor
or internal medicine doctor
Growths at the corner of the eye or on/underneath the eye lid can be caused by an obstruction of one of you eye ducts which normally lubricate the eye. There are multiple different glands at the edge or just underneath the eye lid which can become obstructed and result in a small abscess. A Chalazion is a cyst which develops over one of these glands. Similarly, a stye can also result from infection of one of these ducts. They should be evaluated because sometimes they require antibiotic eye drops or surgical drainage to go away completely. Both of these have the potential to be painful, but they don't have to be.
After you primary care physician examines this growth, he or she may decide to refer you to a specialist if surgical management is required. If this is the case, then your doctor may refer you to an ophthalmologist.