I had
Staph attack a second-degree sunburn once (shins)...the fever developed pretty quickly (two days?), and within five days my kidneys had failed. Throughout the entire two weeks that I was being treated, I had virtually no short-term memory working. Basically, you just lie quietly while you are eaten to death.
Although my early experience of Pain was minimal, so was my ability to function on anything but a rudimentary level (eat, wash, let dogs out, feed dogs, pass out, come to on the floor, go to bed).
An untreated open gash would progress to delirium pretty quickly, so without "magical assistance" there would be no believable way for someone to plan a revenge on their own. Gothic romances use these kinds of wounds a lot to set couples up to fall for each other---the tough guy gets gashed in battle and lies helplessly in a fever while the girl nurses him under a doctor's supervision.
If the cut breaks the skin in any way, circulatory access is established...in fact, pathogenic bacteria culture quite nicely in the lower limbs because they are below the heart. The body is less able to cope with cellulitis (inflammation of the skin) when gravity is preventing free-circulation of blood and lymph.
The medical issues to research found here.
Tetanus does buy you more time, but goes somewhat unnoticed until paralysis occurs. Even if your character pool were familiar with this infection, there in no way to predict the course of disease, so again no way to know how a revenge plan might proceed (unless the villain does not care if his plot unfolds in his absence).
Toxicity to the liver or kidneys via ingested or injected plant residue may be more plausible (a la
Crouching Tiger, Hidden Dragon).
Acute renal failure would certainly result in a fatality where no intensive medical support is available (i.e., any non-modern times). Although extremely painful and accompanied by other gory symptoms, a person may remain functional and able to recruit help executing a revenge scheme (as long as the plant was not also immediately neurotoxic).
For example, see here.