How can i het rid of a stubbon boil that turned into a carbuncle on my scalp without surgery?

Moist heat: What you might try is using moist heat to get it to start draining on its own. The treatment will take about a week and will likely be very painful when you start squeezing pus out of it. The best, safest thing to do is to have your doc drain it. They will make a small incision and make sure everything is drained out over several days, all with local anesthetic. Very safe, the way to go.

Oral antibiotics: Boils are caused by bacteria. Thus, you would need to oral antibiotics to treat this condition.

Don't squeeze: Squeezing a boil before it is ready to release its white blood cells (pus) may be harmfull. Squeezing may cause local tissue damage that may make the problem worse. Place a wash cloth in a ziplock bag, add 1/4 cup of water, heat it in the nukebox and place it over the boil (warm compress). If you are patient, you may see spontaneous "shock and awe" in 3-5 days.