Broken File in Root Canal

One thing that may be hard to understand is that the tooth separated the file, not the dentist.  What this means is that the tooth is likely beyond saving, but in an attempt to save time, money or the tooth, the dentist was being heroic.  We have all been there, so this is not an indication that the dentists skill is inferior.

Often, the broken file will present no issue at all.  The titanium material is similar to the metal used in dental implants, so it may turn out just fine.  A surgical procedure can be done to retrieve it, but it may not be necessary.

Broken files happen. May not indicate anything was done incorrectly because sometimes things just happen and files can break in a tooth .If the tooth was cleaned out well, there may no untoward consequences at all. If you are concerned, schedule a consult with a root canal specialist and see what their opinion would be going forward

Although this happens infrequently, it is not an uncommon complication that can occur during root canal treatment. The fact that the instrument separated in your tooth is not the greatest concern, but rather, how much cleaning of the infection took place prior to the instrument breaking. If the canal was cleaned and irrigated with cleaning solution before the instrument broke, there is a higher likelihood that the prognosis of the tooth is good. However, if the instrument broken earlier on in the procedure and the canal was not adequately cleaned, you may have issues with this tooth in the future.
However, if you just had this treatment done, the discomfort you are experiencing is likely normal post op discomfort. Complications from separated instruments are usually not evident until several months down the road. In any case, your dentist should offer you to see a root canal specialist to evaluate if the instrument can be removed or if any complication arises in the future causing pain or discomfort. Hope this helps!

The best option now is to get see an Endodontist. Is best if they are able to remove the file. 
Once that is done then come back for the crown.

Root canal file breaking happens all the time.  Some cases, the tooth will heal just fine, but some cases the infected tooth will continue to be infected.  We don't know which fate you'll face.  Your immediate post-op pain is most likely due to you just had the root canal done.  If the pain persist or you swell up, then maybe it's time to consider having that tooth extracted and eliminate the infection once and for all.