You should be completely corrected after injection. If you find that the lines are still prominent then you might need more injections in that area. Typically if the lines are deep you will need two cc at least to correct his area. You should go back to your doctor and review the problem together.
The blood vessels that are seen in the skin of the nose can be treated by the V-beam laser or IPL or KTP, but if there is a diffuse hue of redness, that is hard to see in this photo, it depends if the source of that color is superficial or deep. If superficial, then the V-beam laser can be used...
I read your concern. Hyaluronic acid fillers like Juvederm burn when they're injected. You should consider using topical anesthetic for around 20 minutes before your procedure. In my practice, the topical anesthetic is lidocaine / prilocaine / phenylepherine, and lip procedures are well...