I have had this red vein appear on the bridge of my nose. It causes discomfort. Is it easily removed? (photos)

this looks like it may be a dilated vessel but needs to be evaluated in person. lasers and needle can be used to get rid of this quite easily.  best, dr emer.

It appears from the picture that it is inflammation and perhaps matted telangiectasias (spider veins) that give the appearance of a varicose vein.This is an unlikley place for a varicose vein. A better picture would have made it clearer as to what it is.Treatment options for veins in general on the nose and face are topical lasers, IPL, RF, sclerotherapy or microphlebectomy. 

From the photo, it appears that there is a cluster of numerous dilated capillaries on the bridge of your nose.  Often, in this circumstance, there is a central dilated blood vessel from which these smaller dilated capillaries emanate.  These vascular lesion is known as a 'Spider Angioma' are it is, usually, promptly and permanently removed by a laser - most often a 532nm long-pulse 'vascular' laser.  Often just one treatment is all that is required.David Green, M.D., F.A.A.D.Dermatology & Phlebology, Bethesda, MD