True they could be painful at times - chondritis
It is not worth the trouble of removing - time and money and inconveniece, with no guarantee of cure! Operation is only done, when it is pressing on something and causing harmful effects. There are cartilages in other places too - removing is not the solution.
Generally the pain subsides over a few days, when the inflammation subsides - you will benefit from OTC (Over The Counter ( pain relieving/ anti-inflammatory drugs like ibuprofen