Whiley's sister Frances, 53, has diabetes and learning difficulties, which both put her at higher risk from COVID-19.
But last week, Whiley said she had been offered a vaccination before Frances, saying she "desperately" wished her sibling had been offered one first.
Whiley, a radio DJ and TV presenter, said it had been "the worst week of our lives" after Frances tested positive for COVID-19 following an outbreak at her care home in Northamptonshire.
She told BBC's The Andrew Marr Show: "I have no idea why I was offered the vaccine and my sister wasn't; it felt like the cruellest twist in the world because I've been asking for her, wanting for her to have her vaccine for a year, to be honest with you, to be protected.
"Then, for me to suddenly get a call to say that I've got the vaccine, it just felt hideously unfair and she was actually called in for her vaccine last night, my mum got a message to say that she could get vaccinated, but it's too late - she's fighting for her life in hospital.
"It couldn't be crueller."
She added: "It's been the worst week of our lives, without a shadow of a doubt.
"Twenty-four hours ago we were talking palliative care and yesterday she rallied round and we are seeing her oxygen levels rise, so at the moment we have got hope.
"Twenty-four hours ago we didn't have any hope at all, so she is an amazing fighter, she always has been a great fighter and I'm just hoping that her spirit gets her through."
Because of her learning disabilities, Frances had been difficult to treat, with Whiley saying her sister was so frightened that she would not allow medical staff to give her oxygen.
She said: "That is why her oxygen levels plummeted, that is why she ended up fighting for her life, because you couldn't do the most basic simple thing that you would do to try and get somebody through COVID, and we were at our wits' end.
"The medical professionals, who were doing an amazing job, just aren't equipped because it's all so new.
"They don't know how people with a learning disability are going to react in this situation, which is why it makes such sense to just get them vaccinated as quickly as you possibly can."
Asked about the situation, Health Secretary Matt Hancock said: "My heart goes out to Jo and to her sister and her whole family."
Edel Harris, chief executive of the learning disability charity Mencap, said: "People with a learning disability are six times more likely to die from COVID-19 than the rest of the population, yet those with a mild or moderate learning disability aren't prioritised at all.
"We urge the government to include everyone with a learning disability in group six urgently - it is not too late."