Hello and welcome to hcm,
The purple colour at the site of extraction may be due to-
Root/tooth pieces remaining within the socket.
developed due to improper oral hygiene
Bony protrusions also can cause this.
I would suggest you to get a thorough clinical examination by your dentist
An x-ray will help to find out the underlying cAuse.
Remaining tooth portion has to be removed,if present.
Meanwhile,warm saline and betadine
gargle may relieve pain temporarily.