As long as they know you’re safe, and you’re not deliberately trying to gain attention by not communicating with them, I’d say NTA - it sounds like you’re just protecting yourself by taking some time.

You mention that your mum hasn’t responded well to talking about how her behaviour towards you makes you feel, and that you were shut down when talking to her (and your sister) over Christmas. Assuming things haven’t got to the point where you feel reducing contact with them in the long term is the only solution, perhaps you could try writing an email (or even a letter) in order to put your thoughts and feelings down without having what you want to say interrupted.

It’s clear that you’re not downplaying what your sister is going though, and in fact you’re also helping her - but you’re also completely right that her struggling shouldn’t mean you don’t get to share what’s going on with you with your mum.

I wouldn’t want to judge your mum without any further info, but from what you’ve said she does have a bond with your sister that excludes you to an extent, and that’s not fair. She needs to understand that if she wants a strong relationship with you, she has to put in the effort and be there for you.