spider angioma

The condition is called spider angioma; I know because I developed it, too.

During the facial, the "blackhead" was identified as a spider angioma, a tiny overgrowth of a blood vessel protruding through the skin.

A spider angioma (also known as a nevus araneus, spider nevus, vascular spider, and spider telangiectasia) is a type of telangiectasis found slightly beneath the skin surface, often containing a central red spot and reddish extensions which radiate outwards like a spider's web.