We consider the classic online problem of scheduling on a single machine to minimize total flow time. In STOC 2021, the concept of robustness to distortion in processing times was introduced: for every distortion factor, an 12o-competitive algorithm ALG which handles distortions up to was presented. However, using that result requires one to know the distortion of the input in advance, which is impractical. We present the first distortion-oblivious algorithms: algorithms which are competitive for every input of every distortion, and thus do not require knowledge of the distortion in advance. Moreover, the competitive ratios of our algorithms are ~1o, which is a quadratic improvement over the algorithm from STOC 2021, and is nearly optimal (we show a randomized lower bound of O1o on competitiveness).