It sounds like the last eight months or so, since your dad's diagnosis, have possibly been very tough for you all as a family. It can be hard to know what to say, or how to express the depth of how you are feeling - and when emotions are suppressed, it can sometimes lead to feelings of loneliness, isolation and being low in mood.
Tensions may be high in your household at the moment - it is likely that your mum and sister are struggling a bit too, and arguments may spring up and feel hurtful - simply because you're all feeling stressed and upset. You sound like someone who puts on a brave face for those around you? You mentioned that you can feel happy, when you can raise a smile in others, which suggests a caring person who gives more than receives.
It's time to look after you...and it sounds like you might find it helpful to talk things through with someone. Perhaps when the dust settles on your recent argument with your mum and sister, you could say that you're finding things tough emotionally - you may find they feel the same. There may be help and support at school, someone you could talk to about things, or maybe a close friend or other family member.
It might help to have an appointment with your GP, to talk through how you're feeling, and he or she may have someone they can refer you to (a counsellor) - as this will help sort out the feelings and thoughts which are adding to your feelings of loneliness...
Here at riprap, we have some useful counselling and support services links you may like to consider...and you can always get in touch with us and talk through things in more detail...