that is very good that you are taking care of doing a gargle.
Yes you can use mouthwash but they may cause slight burning or irritation,you can use Betadine
gargles 2 tsf in half glass of water three times day. betadine is very good antiseptic and helps in healing the biopsied area .
you can do brushing with ultra soft bristle toothbrush but do not took back as it may injure in tonsil
do take care of the oral hygiene