I feel like I'm being taken for granted. I don't know if I should stay home and care for my parents or I can look for a job and let them be?

My mom is about 64 years old. 4 years ago, she had two brain strokes. Things have never been the same after that. She had been diagnosed with depression and anxiety disorder and had been treated since then. The problem is that, there are so many ups and downs all the time, one day she is good, the other she is not. My last 3 years of my bachelors degree were very hard for me to handle. Now that I graduated I don't know if the instability in the situation would allow me to commit for a job. My dad is living with us. He is 71 years old. He gets ill sometimes but all in all he handles things. He is the one who cooks for us and I support with the cleaning. I don't know what I should do. When mom gets ill, she gets so needy and wants all of our attention and when we don't do that she gets into an episode of crying and saying that she doesn't want to stay with us and that we should do something. We are all tired of this and we got exhausted. I can't get out of home if dad is out and vise versa. One should always be there. When things are not good, I can't study so should I look for a job knowing that me not being there would make my dad collapse eventually. I have two brothers and a sister but they're all married and they visit us once a week. If you have a solution, please, tell me.