I'm trying to translate a proverb that roughly translates to "a wound untreated will fester," but I'm having trouble thinking of an English equivalent.
The idiom a stitch in time saves nine describes the situation well:
Solving a difficulty while it is small may save a great deal of trouble in the end.
A prompt, decisive action taken now will prevent problems later.
One with similar medical overtones is "an ounce of prevention is worth a pound of cure":
used to say that it is better and easier to stop a problem, illness, etc., from happening than to stop or correct it after it has started
There is a slight difference in context, though, as this is more about avoiding problems before they start rather than addressing them quickly once they appear.
This proverb has a virtually identical meaning. See https://en.m.wikipedia.org/wiki/For_Want_of_a_Nail.
In conversation one might say just “For want of a nail!”
For Want of a Nail
For want of a nail the shoe was lost.
For want of a shoe the horse was lost.
For want of a horse the rider was lost.
For want of a rider the message was lost.
For want of a message the battle was lost.
For want of a battle the kingdom was lost.
And all for the want of a horseshoe nail.
Nip it in the bud
to stop something immediately so that it does not become a worse problem (Merriam-Webster)
The reference is to pruning a tree, as you might in an orchard or garden. Branches in unwanted places should be pruned while they're still buds, so the tree doesn't waste energy growing a branch there, and the resulting scar is small.