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.
Following sclerotherapy clot will form in the injured vein. If the vein is superficial and large enough, it will be hard following treatment due the clot within it (whereas previously it was "squishy" with normal blood). Eventually these do improve, but can be tender and even develop discoloration for weeks to months if the clot is not evacuated. The clot can be evacuated with a needle or small incision, or a mini-phlebectomy to remove the damaged vein. These are not deep blood clots, or clots that can cause harm.
