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It is very kind of you to try and help this kitten.
Do not give it OTC pain meds. Cats metabolize these drugs much more slowly than humans or dogs and get toxic side effects easily.
I don't think there is any way to guess how long it will take the kitten to die from its injuries without being able to see it. It sounds like it's been alive for at least 8 hours and is able to move around. It could survive or it could takes hours to days to die without or even with treatment.
I am concerned about your sister getting bitten. Are you in an area where there is rabies. Most of the US has rabies and some areas have a lot in cats and dogs. There is no way of telling if the kitten has rabies by looking at it. If it dies, you should consider getting it tested to be sure that your sister was not exposed.
Let me know if you have follow up questions.