This.The second one.
You were required to complete a medical when your mother was sponsored.
You will not be recognized as a member of the family class because you were not medically examined/declared as part of your mother's PR application. The USA and Canada are 2 different countries so it just does not matter what testing/processes you did for the USA. Your mother's income also has nothing to do with this. You cannot be sponsored as a dependent.
Your only legal way to immigrate is to try and qualify for economic programs but it will take time and money. I highly doubt you will be approved for any temporary visas/permits because of your failed refugee claim. This is why it is pertinent to speak with a lawyer before claiming asylum, your travel freedom is extremely affected when it fails. Instead of being able to cross the border from time to time to visit your mom, it looks like you and her will need to meet somewhere else.