It will depend on why you need a root canal. If the tooth simply needs a root canal because it became non-vital (there's many different clinical reasons for this), then the procedure will be performed through the top of your existing crown. They will drill a hole in the top, do the root canal and fill it just like they would do on a natural tooth. You will have a filling in the top of your crown.
However, if the tooth requires a root canal because of decay under the crown, they will need to remove the crown and remove any decay on the tooth under the crown. This will change the shape of your tooth and make your existing crown unusable. A new crown will have to be made because all crowns are carefully custom made to fit the shape of your tooth exactly.
As for your question regarding the pain, sometimes it does go away... but it always comes back. Unlike most of our bodies, the teeth do not self-repair. The problem will recur and usually with increasing intensity. So you really do need to see the dentist.
But before you worry too much about a potential root canal, you might get lucky and find it's a much simpler problem. Since the crown is fairly new it could be just a need for a bite adjustment. If your new crown is slightly (and by slightly I mean micro-millimeters) too high you could be hitting on that tooth a little bit too hard which can result in a bad toothache over time.
Either way you need to see your dentist. If the bite is off, it will be a quick and painless adjustment. If you do indeed need a root canal, they will start you on antibiotics to reduce the infection and discuss the treatment options with you.
Good luck!
PS. --- Oh my goodness! I'm sorry but I need to clarify some misinformation that was offered by another poster. First, there is no increased risk in performing a root canal through a porcelain crown. It is no more difficult that doing so with a natural tooth. The only risk is the possibility of fracturing the porcelain which doesn't affect the integrity of the crown, just the appearance.The only difficulty is for the dentist finding and accessing the actual canals of the tooth. The same issue arises with a natural tooth.
Second, doing a root canal prophyllactically (meaning to avoid a problem) is not a "recognized and accepted procedure". You would be hard pressed to find a dentist that is willing to kill a tooth just so you won't have to bother with it later. If the tooth shows no clinical indications that it requires a root canal, then there is no reason to do it. In fact it is standard for dentists to try to avoid a root canal. For example, if the original decay was close to the pulp chamber (nerve) there would be a potential for the tooth requiring a root canal, but most dentists will opt to give it time and hope the tooth settles without needing a root canal. In those cases they will sometimes use only a temporary cement on the permanent crown for a few months. But, again, this is only if there is a clinical reason to anticipate the need for a root canal in the immediate future. Needing a root canal after a crown happens sometimes. It is just dentistry. And doing a root canal through a crown is a "recognized and accepted procedure".
Third, if the tooth is abscessed or infected, an x-ray will indeed show this. The only portion of the tooth that is "packed under" is the crown of the tooth (that part which shows above the gumline). And it is true that x-rays will not reveal anything through the metal crown, but, infections/abscesses manifest at the root of the tooth and are readily identifiable in x-rays.
Also, "muck" does not collect inside a properly fitting crown. And porcelain crowns are custom made to fit your tooth with exacting clinical precision. They fit very tightly and any space between the tooth and the crown is filled with the permanent cement. Barring an ill-fitting crown or a crown that wasn't seated fully when it was cemented, you will have no "muck" collecting inside.
I am sorry you are in pain, but you don't need to be frightened by misinformation. Root canals are common procedures and more often than not are also painless procedures. The fact that you have a porcelain crown on the tooth makes very little difference in performing a root canal or in the risks associated with the treatment. Again, good luck.