Severe dandruff could indicate dandruff itself which is significant or can indicate beginning of some other skin condition like Seborrheic dermatitis or Scalp psoriasis. It is also important to prevent their relapse once you have got it cured.
Next Steps
using an antifungal shampoo everyday for first week and then reduce the application to twice a week for maintenance. You should keep the shampoo at-least for 5 minutes on the scalp for it to act. This should solve your problem. However if problem persists, consult a Dermatologist for proper diagnosis and treatment and to rule out any other skin condition