2 long blue veins running parallel down my nose that pop out? How can it be treated?

It’s important to distinguish between varicose veins and spider veins when choosing between laser therapy, sclerotherapy, and vein surgery. With two board certified vein specialists, our center uses a combination of visual examination, functional flow measurements, ultrasound, transillumination, and infrared light to map out vein networks prior to therapy. Lasers can be used to treat deep varicose vein insufficiency, vein perforators, and varicose veins. Sclerotherapy is ideal for spider veins and reticular veins. Whereas surgery is reserved for severely incompetent varicose vein segments.


Best,
Dr. Karamanoukian
Realself100 Surgeon

Veins on the face can be treated several different ways dependent on the location and size. Specifically for nasal veins if they are small surface laser works great and if little bigger sclerotherapy can be performed. Get a consultation with some one who has experience  and good luck with treatment.  

The veins you are describing sound like "reticular" veins, larger than spider veins and 2 -3 mm in diameter . 
As mentioned in other responses, the options for treating these are injections(sclerotherapy), ohmic thermolysis and laser. 
I don't like to inject sclerosing agents into veins around the nose.  These veins in the "danger triangle" are connected to the cavernous sinus through the ophthalmic vein and the ptyregoid plexus. Cavernous sinus thrombophlebitis or thrombosis can occur.  
A laser targeting the blue vessel is the best option in my opinion.  It's painful and it may take several treatments.  Also, it takes about 3 weeks after the first treatment to start noticing results.