hi I am an ER doctor so I can answer what happened.Epiglottitis is an emergency and they would NOT send you home with antibiotics- you would be admitted to the ICU and have IV antibiotics and steroids.You have pharyngitis- likely strep throat.THat is why you have antibiotics to go home.
That flap is your uvela. Some people can touch their epiglottis, but they really gag. And you cannot see it without a special scope.
I hope that this helped.please leave positive feedback if it did :-)