can not move anywhere just like that, It can fall back if someone has severe neck trauma...which u dont have.
Epiglottis can enlarge or swell up if there is infection ....but the infection is or that condition is so severe and painful with unable to breath that person needs urgent medical help
and addmission,,,,which i think u do not have.
So dont worry , and complete the course of ur antibiotics.
Epiglottis can be seen in any individual on making tongue protrude or bring it out to the most possible extent.it is natural.