Does getting a filling / crown hurt without the injection numbing ?

Usually: If you need a filling or crown, an experienced and skilled dentist can give injections these days in a way that you should feel very little discomfort. Much less than trying to do it without anesthesia. There are times when a very shallow cavity can be done without numbing, as I have done, but only under the right circumstances. Ask your dentist.

Usually: A dental injection can be done in most cases with little discomfort. This is much better than trying to endure the discomfort and pain of treatment without anesthesia. Having said that, I have had patients that insist on no anesthetic and did just fine. People have different pain thresholds. It's up to you and your dentist.