You cannot appeal a study permit refusal. You can go through JR to prove an error in law. It doesn’t over turn a decision if you win, all it does it sends your file back to a different officer for review. It can still be refused.
Honestly, you are not eligible for PGWP. You had to continiously study at one school to be eligible but you went back and forth between schools. When you changed to BCIT, you should have continued your studies and graduated from that program. This has nothing to do with parent’s illness.