How long does acute paronychia last?

Depends: If treated with drainage and/or antibiotics it should start to improve within 48-72 hours. Left untreated it is likely to get worse.

Acute paronychia: Acute paronychia usually needs to be treated with antibiotics by mouth. Bacterial infections of fingers tend to spread rapidly along the finger. Damage done by uncontrolled infection may be severe. Usually if infection is severe, the area is opened and pus is drained and culutred, and antibiotics are given for 1 week to 10 days. Improvement is expected in 2-3 days after starting antibiotics.