Modern times. The character has been shot in a non-vital area. It's not a very bad wound; he's not going to die from blood loss or anything. He's on the run and stuck in a shack in the wilderness with another character, who cleans the wound to the best of his ability with the resources available. It's not enough though; infection sets in and he becomes feverish and sick.
I've looked around and found the types of infections that can cause these symptoms (a local infection that progresses to septicaemia seems likely, or would this be too disastrous?), the ways to treat the infection, and the effects of a high fever on the human body. What I can't find is an estimation of how long it would take for a wound that had been cleaned and attended to with only the resources from a small first aid kit to progress to the stage where the character's temperature starts to go up from the infection. I don't need to know a specific time; I know that it would vary wildly according to circumstances. I just don't want to have things progressing implausibly fast. Can anyone help?
Also, all the sites say that if your symptoms get too bad you should go to hospital, and this one gives some advice on how to treat an infection in the wilderness. Mild infections seem to be able to clear up without much trouble, if cleaned and attended to. However, if you don't have access to a hospital or antibiotics, or much else in the way of medicine, is it possible for a systemic infection like septicaemia to clear up on its own? How long would it take, if so? Or is the character a goner unless medical help is found?