Do fillings have to be worn down a little at a time to work?

My teeth were bad, and I had two of my back teeth pulled out, one on each side. Now the first two of the vacant teeth are the material of the previous filling fell out, now the fossa of the tooth is a small hole, the color is a little dark, as if because the material of the previous filling fell out left. Now it’s very sensitive, and it hurts like hell when it’s cold, but there’s no nerve leakage, so I want to fill it as soon as possible. I don’t want to touch the nerve! Does a filling have to be worn down every time? My tooth has a deep sulcus and is very close to the nerve, will it touch the nerve if I refinish it? I don’t want to miss the nerve! Xu Tongkai, Department of Oral Medicine, Peking University Dental Hospital