There are many different kinds of toothache. Some are dull, some are sharp, some are periodic, while some are continuous, nagging unpleasantries. Sometimes they are just sensitive, other times the pain will not go away. Let us try and help identify what is wrong with your tooth based on how it is responding to pain. Here is a list of possible problems. Please, be aware that this is guesswork, and that a real and actual medical diagnosis of toothache and any other problems can only be done by a dental professional after s/he sees you in person.
The enamel on your tooth has worn thin, but you still have your dentine. The sharp pain is because the dental nerve is starting to pick up on the outside world, but there is enough protection that only certain actions reach the nerve. You may need a filling, possibly a root canal treatment.
Your tooth is experiencing constant inflammation, and there is pressure on your dental nerve. Some kind of trauma or inflammation is at work, putting pressure on your dental nerve, your tooth may be infected, or it may be a response to advanced periodontitis. You may need a root canal treatment or just a deep cleaning session.
This means that the dental nerve is under attack, and you need to see a dentist immediately. This kind of toothache only goes away with an extraction or a root canal treatment, possibly an extraction.
This means that your enamel is entirely gone or missing in parts, exposing the dental nerve, but only slightly. The sudden drop in temperature makes the tubules in your dentine contract, sending a sudden, sharp pain reaction to the dental nerve. You may need a filling or possibly a gap needs to be closed.
This is bad news. Although it only occurs periodically, it probably means that your tooth is dead, and you need a root canal treatment, or possibly an extraction.
Remember, these are only guesses based on previous experiences, and there are myriad factors that can influence the diagnosis of toothache, which is a subjective symptom. Only a dentist can tell what the real problem is, but this can give you a way to prepare for what can possibly occur.