First of all, do not go back to that ENT again, and just for now do not go back to your regular doc until you get a good handle on this. Your two choices for docs to see are: Go back to the ER (as imperfect as they are), or go to a group practice of Internal Medicine docs. Son, what you have is a raging ear infection, which has swollen up your adenoids, and could lead to some fairly serious problems if this is not taken care of a lot more decisively and correctly and quickly than has so far been done for you. I am just so SHOCKED by some of these docs! WHEN will they listen when we say, "Sir, it hurts, please, sir."
The reason you cannot breathe thru your nose is because of your swollen adenoids, which they often swell when you have an ear infection. The adenoid lymph glands are located generally behind the tonsils, and inside the head they're right above where the air goes from the nose and down into the throat and lungs, which is an extremely narrow canal. So, it's very easy for the adenoid tissue to swell up enough to block that tube. That's why you cannot breathe thru your nose, since apparently no one can see sinus trouble.
Now, if your adenoids swell up, this prevents normal drainage of any infection in the middle ear, too, which is just above and behind where the eardrum is, and that is why those docs said it looked like your eardrum was about to burst, because there is fluid up in there that cannot escape on down into your throat where all nasal and ear fluids drain, on account of swollen adenoids. That tissue can block both the ear drain tube and nose breathing tube, it's the same one, the Eustachian tube.
Now, adenoids swelling up can happen for several reasons, upper respiratory infections, sinus infections, ear infections, adenoid infection itself, bacteria, virus, allergies, you name it, whatever might irritate your throat, nose, or ears will do it. Treatment can be antibiotics (perhaps, tho, the Omnicef didn't work, in which case Amoxicillin is another choice), and new prescription ear drops to better relieve pain, and if worse comes to terrible they can surgically put some tubes in your ears to allow for drainage of the infection pus in your ears, like they do for little kids.
And in fact, it is very important that the infection not build up too much, might affect your eardrum function! In addition to ear drops, your Tramadol ought to cut back on the ear pain a little, but I'm telling you and as you know, an earache can be unbearable, so you could ask the doc to give you something stronger, or you can ask doc if you can double up on the dosage of your Tramadol if you want. Aspirin is a good anti-inflammatory, too, just take it with milk.
Normally if an ear infection is cleared up (which since the ER docs said your eardrum was about to burst, then I HAVE to assume you've got one heck of an ear infection), which is precisely what causes SO much pain, but when that's corrected, the adenoids should go down and you can breathe again. Whilst your ears are being treated, you can drink orange juice, gingerale, and gargle with salt water to help ease the inflammed adenoids. BUT sometimes the adenoids just won't settle down, in which case a doctor can do surgery and remove the adenoids. It's not unlike removing tonsils.
The worst of this whole thing is, the ENT you saw apparently knows nothing about how adenoids swelling up can prevent you from breathing thru your nose, knows nothing about ear infections, and I'm appalled that he so cavalierly sent you off with prednisone, and this is because if an ear infection isn't cleared up, by golly it can get mighty serious in a big hurry, by actually infecting the bone around all this infection, and even turn into meningitis, not to mention the possible ruptured eardrum calamity.
So, let us know where you decide to go to pursue this thing, and especially since you are now armed with some information about what adenoid swelling can do to a person, not to mention your ear infection is still going full-blast, then I'd really like to know what sort of treatment is given to you THIS time. I'm sorry you got pushed around by a bunch of very tired and apparently unedu-bi-cated folk, but you know the score now, so I am very hopeful you will get well soon.