What's the Name of That Book??? discussion

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Rocco
SOLVED: Children's/YA
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SOLVED. Y/A Man and woman in a cave. [s]
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I tried to link to it but my computer wouldn't bring it up correctly
The cover was maybe a yellowish white colour and had a drawn figure of a woman on it. I'm not sure whether the genre is Y/A, it could be romance or science fiction.
I don't remember much about the plot, but remember that there is a young man who somehow finds himself in a cave in poor condition. He is being rescued/looked after by a young woman. The genders could be reversed here. At night she has a fire made and makes him food/broth.
The book is set in a very bleak and barren environment. I'm not sure whether there are any characters other than the young man and woman. There is a vague memory of either a tribe or a man which is older and wiser, though they could be from a story that the woman is telling the man while they are in the cave.
It's at the end of the book where it's revealed that everything takes place in a world after nuclear war has destroyed basically all of civilisation.
What I remember sounds a lot like this stackexchange question:
https://scifi.stackexchange.com/quest...
I'm quite sure that what I read was a book of a few hundred pages though, rather than the short story which is the accepted answer.
Thanks!