My iPhone just shut down whenever I plug in headphone

It sounds suspiciously like an issue with the charging port itself. There are several connections within the port and it seems on your phone the pins associated with charging the phone are working fine, but there seems to be something shorted on one or more of the data lines used for communication. Have you tried plugging it in to a computer to see if it's recognized and can talk to iTunes? If it can't that would be further evidence of an issue with the charging port.

First thing to do is to clean the charging port; generally something like 90% or higher concentration isopropyl (rubbing) alcohol, an eyeglass cloth and a toothpick can usually get in and do a good job of cleaning the port. If you have a can of compressed air that will help as well. Check it carefully with a magnifying glass and a bright light to make sure there isn't any lint or debris in the port and that the pins are all present and undamaged.

Next, check your headphone connector for any evidence of shorted wires or damage to the cord. If possible, try the headphones in another phone to make sure they work, and try a different set of headphones in your phone; that will tell you whether the problem is with the headphone or the phone itself. As I mentioned, connecting to a computer could help figure that out as well.

If all that doesn't do the job or you find evidence of damage, you may have to resort to replacing the charging port. Sorry to say iFixit doesn't have a guide for that repair on your phone, but there's a Spanish site called Nadie Me Llama Gallina that has just what you need.

Manuales / Apple iPhone Xs Max / Flex with load connector and lower microphone - Nadie Me Llama Gallina

It is, of course, written in Spanish, but used with the Chrome browser's translation feature it is quite usable and well written.

Check it all out and let us know what you find. Good luck!