I mean, you (presumably) don't have a tail, but many animals do, and feel pain when something hurts their tail. If you have a body part with the ability to have a sense of touch, your brain is just mapped to know which part of the body is experiencing that sensation when you experience it automatically. (See also: What Is It Like to Be a Bat?)
AdventZero said:
Imagine biting your own arm off to rush to a friend's aid.
A wolf will bite its leg off to escape from a trap, as it is better to live with a limp than die of starvation. When a bee stings, it will die shortly after it tears its stinger off, but will choose to lay down its life for the hive unquestioningly.
Although that said, Chompy's loyalty is pretty notable considering as she's apparently known Bowsette for what seems like an hour or so, yet is willing to risk death and inflict significant bodily harm on herself for Bowsette. Like with the question I had earlier about how much time Bowsette has had to earn her character development, there's a point where Chompy starts to look less like a loyal friend and more like a martyr just waiting for a cause.
A wolf will bite its leg off to escape from a trap, as it is better to live with a limp than die of starvation. When a bee stings, it will die shortly after it tears its stinger off, but will choose to lay down its life for the hive unquestioningly.
In the bee's case, they normally don't lose the stinger when they sting other animals. It just so happens that human skin is too rubbery that they can't pull their stingers out without ripping out their guts in the process.
In the wolf's case, I agree. A wolf would rather risk being maimed to escape certain life-threatening harm. In Chompy's case, she's risking maiming herself in order to rush into harm's way. That's saying something for a girl who's just been born (into her current form) for less than a day.