How can I treat a vein in my upper lip?

It is very difficult to answer your question without a picture.  In general lip veins can be treated by topical laser.  

Hello and thank you for your question.  Veins in the lips can usually be successfully treated with either IPL (such as the Icon MaxG) or laser (such as the Icon 1064 laser).  They may take several treatments to successfully resolve.  So there is hope.  I would recommend consulting your local aesthetic physician for more advice on treatment.  Good luck!
Dr. Fleming