It sounds as though your mum's cancer has been a feature of you and your family's lives for a long time. Now that she is more unwell, it is natural that stress levels for everyone concerned have increased. Both you and your stepdad want to do the best for your mum, but caring is hard work, both physically and emotionally.
Your stepdad has probably got little patience for much else at home, but that has a knock on affect for you - as this is your mum, and seeing her less able to do the things she did, are understandably upsetting.
Perhaps ask him if he'd prepare a list of jobs that need doing, and then you'll know what will help. Acknowledge that he is probably finding everything stresssul at the moment, and you do want to help. Explain that the situation with your mum is upsetting for you too, and that's why sometimes it may seem (to him) that you're not pulling your weight.
He , in turn, may be so wrapped up in what's going on, that he can't see how upset you are...
Have you anyone to talk to in the family, friends, or at school/college who you can talk to? This is an emotionally draining time for you, and a lot to carry on your own. Negotiate with your stepdad and mum for time out of the situation, so you can see friends and feel a normal teenager for a while, without the 24 hour pressure of caring.
Your mum, although less able to talk and walk, will probably still enjoy your company, help and support - even if she can't express what she feels. It can be distressing seeing someone you love and care about getting more unwell, but she's still your mum, and that won't change.
I hope you'll feel able to message us here at the riprap team (using the 'get in touch' form), if you'd like to hear from us for support, and the chance to talk through how things are going.
Warm wishes
Sue