Thanks for asking the query,
Bleeding gums in your child is due to inflammation of gums known as gingivitis
It occured due allergy
to the antibiotic you have given or due to poor oral hygiene , vitamin deficiencies .
Consult to a Pedodontist and get checkup done.
Get complete mouth scaling done .
Develop the child a habit of brushing twice daily with a soft bristle toothbrush.
Use saline water gargles 3-4 times a day.
If the antibiotic is not suiting you , get it changed.
Maintain a good oral hygiene .
Hope this helps out.