i had something similar . however i was on a cpap machine , the pressure cause irritation to the Eustachian tubes , eventual the ear drum ruptured and the fluid started to drain from my ears . the medication they gave me did not work , they took a culture with a swab and identified the infection, with the new ear med's and discontinued use of the cpap it cleared up however the ear drum still needs to be repaired and as of yet my hearing has not returned , the ears nose and throat specialist said he has a good chance of repairing it for me ,
my advice would be to get a new test on the infection to find just what the infection is and what exact drug is needed. also see a ENT to have your ears properly checked cleaned and tested. PS i was also advised to keep moisture out of the ear when showering water helps bacteria
The antibiotics will probably get rid of the ear infection, and maybe the sinus infection (sinus infections work differently than ear nfection), but if your Eustachian tubes are closed, which it sounds like they are, they may take longer to open up and recover.