It's not your epiglottis you see in your mouth but your uvula. I think the epiglottis is the flap that closes your airway in your throat.
Your uvula can get swollen and make you feel like you have a lump in your throat. If you also have throat pain I'd see your doctor to see if you have strep throat. Other than that there really isn't much you can do besides see an ENT to have it removed if it does it a lot.