I had a lower molar extracted. A while later a developed severe discomfort in the general area of where the tooth had been, So much discomfort that I thought another tooth would need to be extracted. It turned out that the problem was a root tip that had not been removed when the tooth had been extracted. The dentist informed me that such pieces of extracted tooth can move and start working themselves out of the gum, causing severe discomfort in the process. So its possible that a mobile tooth fragment can cause a lot of discomfort, requiring its remova,l even in the absense of an infection.
In humans, a blood test would often show when we're battling an infection as our white blood cell count ought to be appreciably high.