The dentist said you have an absessed tooth does it have to be pulled or can it heal?

No. Generally speaking an absessed tooth can be saved by antibiotic therapy and root canal therapy together. There are times when a tooth cannot be saved though- when not enough tooth structure is left to support a crown or "cap", or when a root is actually fractured. Sometimes an absessed tooth is caused from a periodontal problem or in other Words, a gum problem. This requires antibiotics and debridement or "deep cleaning" - or surgery.