i don’t know exactly what type of ticks you have in South Africa, but generally a tick will not just bite, it will embed its mouth-parts into the bitten animals and execrete a form of cement that makes the tick very difficult to remove until it has had its fill i e a good blood-meal. If the tick you found was just little it perhaps hadn’t eaten yet?
Most warm-blooded animals can get Lyme disease but the symtomps generally takes several weeks to emerge.
Relapsing tick fever has a week’s incubation period, so if the symptoms and the tick occurred at the same time that would not be it.
There is a form of paralysis that can occur with tick-bite in sub-saharan Africa. But the progression of the paralysis stops as soon as the tick is removed and the patient then recovers.
(I did a MOOC in tropical parasitology some months ago given by Duke uni, that is my source of info)
A lethagic bunny makes me think more of GI stasis, unless she’s eating, drinking peeing and pooping normally that is. http://www.bio.miami.edu/hare/ileus.html