The pain will normally go away in less than a week or so ; but, If I were you I'd get it x ray'd at the dentist as soon as you can. You might as well know the truth about what's going on because even though you'll have no pain, have no illusions about it. There's a good chance you are sitting on a problem that needs to be dealt with.
Mainly, there's a chance the nerve has died and if so, you need a root canal. Otherwise you'll be sitting there with a dead tooth in your mouth and the longer you let the dead tooth sit there the more likely it becomes that it can't be saved with a root canal.
The cost of a root canal varies but budget around $950 or so and then a crown will run you another 700. Total around 1650.
If you have an infected tooth and let it go too long the root canal option will not be there because the more rotten a tooth becomes on the inside the more difficult it becomes to save it with a root canal.
And BTW you won't feel any pain while a tooth is slowly rotting away from the inside.
If the tooth becomes un savable via root canal your best option is a dental implant for about $3800. Other options are a bridge for around 2300 but those are messy and dirty and need to get redone every 6 years or so. So bridges are a bad option relative to dental implants.
Other option is a denture for the gap that would be left after a rotten tooth has been pulled. That would be maybe 500. or so.