The vein that appeared after having varicose surgery is like a string it is very hard and goes down the head to reach the left side where surgery done?

Varicose vein: Did you have a vein sclerosing or stripping procedure? If you had the vein sclerosed, it is expected to scar and harden for a while. Do you mean the "head" of the vein or your head? There should not be any varicose vein surgery done on your head. This would be extremely dangerous as there are many central veins that do not have valves and you can embolize the cavernous sinus in the brain.

Hard string vein: This is very likely a "dead" vein that will gradually absorb over a period of several weeks to a couple of months. Veins that are hard / firm and like a string (and often tender) are consistent with dead or dying veins, such as after a vein laser treatment or radiofrequency vein treatment. The body softens & absorbs these over time. Other possibility is a phlebitis. Recommend vein ultrasound.