What are the causes of red itchy bump around the eye?

Chalazion/hordeolum: Most often, this finding would be the result of a blocked and infected gland or hair follicle of the eyelid. Depending on the location, it could be called a chalazion or hordeolum (stye). Treatment with warm compresses will resolve many of these lesions. See an eye md if the bump is not resolved within a few days of using warm compresses, or anytime if it worsens. Some need to be drained with surg.