What is your insulin regime with Novorapid? How often are you taking it and how much are you taking?
Novorapid is a "fast acting insulin". This means on average (everyone is different) it reaches its peak potency about 30 minutes after it is injected and lasts in your body for about 4 hours.
It is usually taken with food to lower the BG rise associated with carbs. It can also be taken to lower BG.
It is a very common insulin taken by people with type 1 diabetes. We also tend to take a basal (background) slow acting insulin once or twice a day.
I do not know about it being taken for type 2 and have not heard about it being taken without a background/basal insulin ... but that could just be my ignorance.