You might want to see a dermatologist and see if you have rosacea,
That is exactly what I thought when I read the description.
I have a naturally "rosy" complexion and now I have those thready-capillary things on my cheeks as well - more on the right side than the left.
My derm told me it *is* rosacea and that regular use of something like MetroGel or Finacea will help alleviate the symptoms. However the capillaries that are already there will have to be removed by laser therapy if I want it.
I checked with my insurance and can't get a straight answer as to whether or not they'll cover having them lasered, but if they will, I'm going to have it done. In the meanwhile I use Finacea cream which I put on under my regular moisturizer every morning.