is it desperate for my laptop fan to run constantly?

No not at all. You should be asking this if the fan DOESN'T run constantly. The fan is designed (and locate there for your laptops safety) to keep the air flow going. If the laptop is hot it will run faster than if it was cooler. Either case, it has to be running. If it doesn't then it means the part is damaged and you condition to have the fan running or if you overheat a computer, it can damage everything inside.

Pious luck!