Pax,
If, as the others already suggested, you have the option to take FMLA, I can tell you that it can be just what you need in these kinds of situations. I knew nothing about FMLA in 1997-8 but my employer at the time offered it to me after learning about my struggles at home. Back then I was constantly trying to stay one step ahead of my father's deteriorating health. My employer and I worked out a plan to work from home where I could keep my eye on my dad. I took no pay cut all the while on leave. Consider discussing options with your employer if your work is something you can do remotely from home. Today it's a lot easier and more accepted to work remotely. Perhaps you can ask for even part-time work from home, to alleviate your crisis.

If I can offer any advice at all, I urge you to please force yourself to dedicate some time daily solely for yourself. Even if that's just 10 minutes a day - this type of stress caring for a parent can be debilitating mentally and/or physically. If I didn't have my passion for distance running back then, I would have fallen deeply into depression (as it was, I was not in good shape emotionally). You need to give yourself some time to decompress from that kind of stress or it will take a toll on you. It's vital. If I can offer any advice at all, let me know. PM me.