(Warning - novella-length post ahead 
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The other member of this household managed a nurse bank for many, many years in our local hospital. Under duty of care, if someone was as ill as you sound, of course you wouldn't be expected to come in! Risk of infection for the people being looked after would also be something of a factor...
For what it's worth, my other household member left the NHS (long story but basically when they left their job, which they were constantly told they were cr*p at despite consistently recruiting excellent staff who often went on to become permanent employees, they were replaced by four people. Two of whom were automatically put on the next band up. The hospital had refused to upgrade my friend for several years, despite the fact they were evidently doing the job of four people. At the point my friend left the hospital had especially stupid HR who did other things like promote someone from a Band 3 to a Band 7 without either advertising the job or going through any interview process, because this particular Band 3 had a "face that fitted"). Anyhoo, the nursing staff bank at that hospital, and many others, is always recruiting. There is massive demand for bank staff, in the NHS and at care homes. Have a look at the NHS jobs website when you're a bit better, you might be quite surprised. And even as bank staff in the NHS, you still get to pay into what is a good pension scheme, and you also usually get very good training and access to the other staff facilities at your Trust. Plus discounts with some shops and businesses.
When my friend left the NHS, she worked at a local care home for about a year; when their deputy manager, who was excellent, left, the home rapidly went downhill, but even the toxic company running that home has a bank of staff they can call on in case people get ill, and they use agency staff if they can't fill a shift from their own bank.
When she left that company, my friend went to work through one of the big nursing agencies and has never been happier or more relaxed; very occasionally the agency she is with has requests from families for direct care although most of her work is in care homes. This agency alone has masses of work; she sometimes has to turn shifts down. She has been offered permanent jobs several times but she much prefers the flexibility and the fact that when you're agency you're less likely to be emotionally blackmailed or get involved with the petty politics. You also get to see some really good practice (and some really bad practice) and get a real feel for where the good places to work are.
Your employer is not being reasonable. People get sick. Things happen. Life is not a nice, safe, predictable straight line. Maybe have a word tomorrow with one of the nurses or the doc and ask them if they think going back to work is a good idea when you're weeing blood and in such a lot of pain. I would put money on their answer being, "Absolutely not". The NHS doesn't give morphine for just anything, so your pain levels must be very high. They don't give antibiotics for just anything either, so there is evidently infection which I'm sure they'll get to the bottom of and sort out. But it might take a little bit of time.
When you're feeling a bit more with it I'd be inclined to send a response along the lines of "The team of registered medical professionals taking care of me here in the hospital, including doctor/consultant/nurse, strongly advise against my returning to work until I am better. At present I am passing blood rather than urine and my pain levels are approaching ten on the pain scale. The hospital staff have also put me on morphine. Apart from the fact it would be detrimental to my long-term health to return to work again prematurely, as the pain is making it difficult for me to concentrate and make decisions, I would be concerned about potentially making an error in your sister's care. I'm sure you wouldn't want that".
And seriously, when you're better, definitely look for another job. Even the NHS would be better. And I don't know where they got that "48 hours" rule about being ill, never mind the "this is how all care jobs work" rubbish. I don't know about you, but I wish I could see 2 days into the future!
There's some quite useful information at www.which.co.uk/later-life-care/home-care/organising-home-care/how-to-employ-private-carers-aszsg4j2q80m that might help you and at www.disabilityrightsuk.org/being-control-getting-personal-assistants-pas although if you are already employed by an agency the rules might be slightly different.
Hope you feel better soon - I know it's a cliche but you're in the best place. 