From your description, it sounds like you have a spider naevus or telangiectasia on your facial skin. Both of these are fairly common and thankfully do not cause any health issues. They may however be a marker of other underlying problems, especially if there are multiple such vessels. I would advise that you seek help from a dermatologist to properly diagnose it first of all.
In terms of treatment, either lesion can be effectively and safely treated with the VBEAM pulsed dye laser, which shuts down and lightens the vessel. Usually 1-3 treatments may be required.
Hope this helps!
Warmest regards
Dr Stephanie Ho, Dermatologist