You will come out of this knowing a lot more about stress and its impact!
Perhaps also worth sorting out what you want. Do you want practical help either directly or to allow you to look after your parents, or simply some looking after of you.
If you dont know, others won't either.
The latter is important, and there will be people around you who will want to do something. Cake from children, flowers from friends, a sympathetic ear over a 
or 
. And us! Just let people know. Friendly staff in a restaurant just down the road from my mum's made a huge difference as I was able to clock off at 6.00pm and unwind. My cousin found similar in a cafe near her dads.
In terms of practical help, can any be delegated? For example a cleaner or someone else known to your mum or dad be paid to run some errands. A paid carer. I now have a small network, and indeed a one point last year when it looked like I needed to be there in person to sort something minor out, a MNetter offered to help. Is there someone sensible within the health/care network you can use as a sounding board. And do let them know you are floundering. Praise and sympathy for professionals was really valuable. I think it was pretty standard to jolly along relatives caught up in a crisis, but because you have a medical background you may not be getting the same level of back-patting.
On a similar theme, when it all started kicking off, I invited my GP cousin and his wife round for dinner. I was starting with no knowledge at all so they took me through care options etc, but also gave me the talk about being "good enough" was sufficient, and that all I could do was make what seemed to be the best decision at the time. Only time would tell whether it was the right decision.
And be clear to your family that your priorities lie elsewhere and they need to rise to the cooking/cleaning challenge. DD impressed friends by turning up to Extra Curricular in a (pre-booked) mini cab. (Off topic a bit, but amongst some groups of West London teenagers Addison Lee does not really cut the mustard. If you can't boast of a family driver, its limo service or, better still, your own limo card.) I found house clearing was much faster and nicer when DH came with me and we could take a break from house clearing by goiing for a walk or out for a nice meal. DS came down over Easter, and away from the internet was able to crack on with lots of past A2 papers, as well as help move furniture.
Make sure you have somewhere nice to stay. You can negotiate very cheap prices on off-season holiday accomodation.
Your work colleagues too probably need to be told how they can help. This is a tiny proportion of your working life. Your mum is the priority. Would it be simpler to ask for the month off, and have your colleagues find a locum. You will be exhausted and are likely to take months before you are back to full fitness, so they should see it as a investment.
Ahh and decisions making. Buying into sheltered housing, sorting out finance, house clearing, let alone care. There were so many decisions. And all on behalf of someone else, within a strange whirr of emotions. At the time I read an article about Barack Obama who apparently belives you can only make so many decisions in a day. So on a daily basis he has others choose what clothes he wears and what he eats, so he can focus on the important stuff. I kept hitting decision making paralysis, so this chimed. DH, in contrast, thought it was barmy. I agree though with whoever recommended writing things down, and making lists. Stress, I know, but my memory seemed to be almost as bad as my mothers.
(Actually looking back, I did burst into tears quite often. But mainly in banks. Banks, and their bureaucracy, were the low point!)