is because after extraction the blood clot got dislodged from the socket.
so ideally the dry socket should be curetted which means it should be cleaned & irrigated with medicine & obtundent dressing which is already given to you must be placed.
the brown discharge or paste is the dressing. it will take around a week for the pain to subside. you should go for regular dressings, & maintain that area clean. food lodgement in the socket can again cause infection & give more trouble.
mouthwash twice a day to help in healing. betadine should be diluted with equal amount of water, & after rinsing with it you should not intake water for atleast 20 mins.