If there is still infection after the root canal and antibiotics don't treat it, what are symptoms of it, and does that mean the infection has spread?

Infection: Swelling/pain/fever are general signs of infection around the tooth or radiating to a adjacent area. Also a dental radiograph of the area would be very helpful to diagnose.

Fractured: The is most likely a crack in the root and will not be resolved until removed. Preferably with an immediate placement of an implant.

Root canal complicat: The symptoms of a tooth not responding to root canal treatment can be pain, swelling or a bad taste in your mouth from the infected tooth which usually you can see a small pimple on the gums by the affected tooth. The infection can spread to adjacent teeth if left untreated.

Same symtoms: If the tooth that had the root canal was infected bad and infection spread beyond the root into the jaw bone then you can still have residual infection after completion of the root canal. In this scenario you need additional antibiotics to treat it or it will spread. If there was a problem with completing the root canal properly you may still experience infection. Go back to dentist if this is so.

Infection: If you are having pain/swelling/fever/bad taste after root canal Rx, and antibiotics ineffective, would suggest you see a root canal specialist, an Endodontist, as existing root canal Rx probably failing. Yes, if there is infection it is spreading via circulatory system to rest of body.