I went too the doctor because i hurt my ankle and they said it is sprain but it's been purple for 3 days could they be wrong?

Possibly: Sometimes fractures around ankle can be subtle and not obvious. If discoloration and pain persist you should consult again your physician. Sometimes repeat xray exam 7-10 days after trauma will show healing fracture. Some people need to be casted even if do not have fracture, for severe sprains.

They could be: But skin discoloration does routinely occur with an ankle sprain.