Mild tooth sensitivity is very common and is quite normal to suffer from time to time, if you are suffering severe tooth sensitivity then this would indicate a more serious dental condition such as a broken or cracked/chipped tooth or tooth decay which is disturbing the tooth pulp causing the sensitivity, or even a recent or new filling will cause tooth sensitivity.
Mild tooth sensitivity is caused by the gradual exposure of the softer part of your tooth that lies under the tooth enamel, called dentine. Dentine has tiny tubes that lead to the nerve and are filled with fluid (the tooths nerve is protected by pulp tisuue). Eating, drinking hot, cold or sweet foods and drinks can cause a change in fluid movement. This fluid movement causes the nerve endings to react in response, triggering a short, sharp pain (normal tooth sensitivity the pain should quickly subside).
Recent or new fillings will always give discomfort/sensitivity for the first few days, especially if the filling is close to the tooths nerve. Sometimes a dentist may have to drill to far into the tooth if the decay is deep, this then may damage the tooths pulp to much for it to recover. The tooths nerve will then be open for infection (abscess) and slowly the tooth will die, thats if the pulp cannot recover to protect the tooths nerve. If this happens you will need a root canal to save the tooth, but the tooth will still be dead as their is no nerve, the tooths nerve is taken out during the root canal procedure.
There is a condition called Pulpitis, there are two types ''Irreversible and Reversible'' Reversible pulpitis is generally characterized by sharp sensitivity to cold, sometimes to sweets and sometimes to biting. Usually heat doesn't bother the tooth as much. Irreversible pulpitis is a severe inflammation of the dental pulp where the pulp tissue cannot recover and the tooths nerve is effected causing it to die.
Basically is you are suffering from mild tooth sensitivity and you have not had a new filling or any other recent dental work, then you may want to use a toothpaste specially developed for sensitive teeth that helps protect the dentin and those tiny microscopic tubes that lead to the center of the tooths nerve.
If the pain is severe, you may want to see your dentist to check your teeth for cavities, decay. Any tooth with an old filling may have under lying problems such as leakage/decay under the filling, the tooth may have a microscopic hairline crack due to an old filling (micro-cracks do not always show up on x-rays).
I hope you can get the correct treatment and feel better soon.