What can I do for my dry socket without going to a doctor?

Not much. A dry socket will present as intense/increasing pain typically 48 hours after a tooth extraction. It is caused by exposed bone in an area that has lost it's blood clot. Treatment is to have a medicated dressing placed into the affected area. Antibiotics will not help a dry socket. Some patients have 'waited out the pain' without seeing their surgeon; I would not recommend that course of action.
Dry socket. See your dentist/oral surgeon again. Dry socket occurs when the blood clot at the dental extraction site is dislodged or dissolves prior to wound healing. Pain results from exposure of the bone & nerves. Otc treatment is inadequate for the problem. The surgeon will remove food particles and pack the wound with a medicated dressing that may have to be changed every few days. He can rx pain meds.
I can not help you. Need more information, which socket you talking about?