First of all, I am really pleased to hear that your mum has got the all clear about the cancer. I am sure you are all extremely relieved about that, and maybe because of this relief - and you don't have the constant anxiety about your mum anymore - now you can somehow allow all these other emotions to come out. Maybe emotions that have been there all the time but that you have been suppressing because you were mostly concerned about what was happening to your mum.
We often find that the children can be quite unsupported and feel quite neglected when a parent has cancer and may be going through tough treatment. This is partly because it is only natural for everyone to focus on the person who is ill and partly because people often feel very helpless with regard to how they can support children in that situation. Maybe even more importantly - children can be very good at hiding their emotions and put on a brave face - pretending that they are coping okay. We find that children/teenagers are very caring and concerned about their ill parent and try to behave in such a way so that they are not adding to their parent's burden - they don't want to make them any more upset than they already are. Then of course, many teenagers are going through a phase when they may not communicate very openly with their parents anyway and therefore tend to keep their emotions to themselves.
I think that what you are assuming is correct - people are so relieved that your mum has got the all clear that they can't see any reason not to just be happy about it all. Of course you are happy as well, but I think that what you really need is some recognition of what you have been through. Yes - your mum has got through it, but you have been through a terrible time as well - and you have not had the support you have needed in that time. Because you don't want to be selfish and unappreciative of the good news, your frustration is probably coming out now through the arguments with your mum. As you say, they are probably just silly things not worth arguing about but this is your way of getting it all out and to claim some attention for yourself. I think what you are hoping for is some understanding and support for what you have been through and then you would feel ready to move on and appreciate even more the fact that your mum is okay again.
You should talk to your mum about this and explain why you feel tense and argumentative and talk to the rest of the family as well. There is no point making people feel bad about the fact that you missed support when you needed it, but it may help them understand that you have been through very difficult times and you can't just press a button and then everything is okay. You need to know that they can see things from your point of view before getting back to a new life after this hugely distressing event in your life.