I don't want to look after my mother in law
Do you not have a good relationship with her?
I don't. She's been a bitch to me ever since her daughter, my wife, introduced us.
You should always be there for your family, even when you don't want to, so it's wrong not to look after an in-law who needs help.  You can find ways to let her know politely if she is doing things that annoy you.
It's just my mother in law, she's just an annoying person who doesn't know when to shut up and I didn't do anything wrong so I should be able to look after her whenever I want
Even so, you should look after her if only for your wife's sake and peace of mind.