A dry socket will develop after a tooth extraction and after the tooth extraction the pain should lessen over a few days.
If the pain gets worse then it's likely the dry socket that you mention. Most times a dry socket will go away within a few weeks on it's own but it's best to go back to the dentist to have the dry socket treated to make it go away faster.
Leaving a dry socket untreated could lead to complications and infections of your gums.