I had anti bs for an infection under my crown three weeks ago, my dentist is on holiday and im not booked in to have it extracted until mid/late ...

Emergency: There should be someone covering your dentist's office while they're away. If not, you'll have to make other arrangements.

Murphy's Law: It's a corollary to Murphy's Law that acute dental problems happen when your Dentist is out of town. As you are in distress, better to have it treated now than waiting. Your Dentist probably has coverage arrangements, and you can get that information by calling his office. Or you can contact an Oral Surgeon to have the tooth extracted. Then see your Dentist to arrange tooth replacement.