Hello, wound healing after cauterization may take few days depending on size of the area cauterized and amount of tissue removed. Normally it should heal within two to four weeks. However you may see some swelling, redness or mild pain, however depending on the exact surgery, you would see scar tissue afterwards. As you mentioned about white skin, it may be scar tissue, and that suggests, that healing is taking place well. As you are already changing your dressing everyday and keeping it away from dirt, you are doing exactly what has been adviced to you. So I guess, you should keep doing what you are doing and not worry about the healing process, however if you see, too much of redness, or warmth, or swelling or pain on that site, you should immediately consult your dermatologist.