If your tooth is throbbing and is sensitive to hot/cold, it most likely means you have a large cavity in it that requires a root canal.
If you are experiencing throbbing tooth pain, you are experiencing a toothache. However, you would need to see your dentist so he/she could examine and take a radiograph to see if it is decay and restorable, requires a root canal (saves the tooth), or requires you to choose an extraction ((loses tooth). But if there is also swelling you could have an infection and should seek treatment immediately.
Ellen Harrison Finn