Some people did survive injuries in the Medieval period, but stab wounds are more likely to be a problem as infection goes in deep. Cats get really nasty puncture wounds from biting each other when fighting.
The reason cat bites infect most of the time is because cats' mouths are absolutely 'filthy' with pathogenic bacteria. Same with monkeys and humans. Dogs, not so much. Dogs can rip each other up in a fight far beyond what cats can manage, but about half the time the resulting wounds will not become infected (even if very deep). Knives are not inherently 'filthy' either. The knife you just used to gut a deer or smeared with feces, yeah. The knife that's been cleaned and oiled, not so much. (Bacteria needs nutrients to thrive. Steel kinda lacks this, and oil may inhibit growth.)
In any event, in a fantasy world I don't have a problem with infection control as separate from other 'healing'. What the OP has in mind sounds reasonable to me. Just be consistent about it.
As to how disabling it is for how long, there are factors other than just the size and placement of the wound. Movement that prevents healing can be an issue, as is individual pain tolerance. Fudge factors like "lucky it didn't cut anything major" and how much she can tolerate before she
has to stop moving can be adjusted as required.
I'm reminded of a ML baseball player who'd suffered a microtear in the small muscles between the ribs (we're talkin' maybe a quarter of an inch). Most of the time he was fine, but if he'd swing and miss, it hurt so bad he'd go down in a heap and couldn't get up for a couple minutes, and this was a tough guy who'd shrug off being nailed with a 90mph fastball. This went on for several months, then it healed literally between one day and the next and that was the end of it.