A cough running 10 days with fever starting later, especially when amoxicillin hasn't helped, points more toward a viral illness than a simple bacterial one, though a secondary infection is possible. Since pregnancy is a real possibility here, that needs to be confirmed first, because it changes which medicines and tests are safe to use.
Next Steps
Take a home
pregnancy test now rather than waiting for the cough to settle. Paracetamol is generally considered safe for fever in pregnancy, while ibuprofen is best avoided. A chest X-ray can still be done with abdominal shielding if needed. Please see a physician or obstetrician so amoxicillin can be reviewed and continued or changed based on the test result.
Health Tips
Seek urgent care if she develops breathing difficulty, severe weakness, a fever above 102°F that won't come down with paracetamol, or starts coughing up blood.