hello and welcome to hcm forum,
i would like to inform you that drainage
is very important in order to resolve the infection, opening from where the pus discharges is called sinus
and as the infection in your fiance's case must have been severe therefore the sinus is present extraorally.
also,he cannot swallow the discharge, and he is on antibiotics therefore you don't have to worry,
the swelling as well as sinus will resolve with time.
just take care of his diet and make him eat well,
i wish him good health.