Teething is not a diagnosis of exclusion for fever. When a baby has a fever, the reflex to say "must be teething" is understandable but potentially dangerous. Fever always deserves its own evaluation, especially in young infants.
It is better to over-call than under-call. Pediatricians would rather see a baby with "just teething" than miss a baby with an evolving infection. If you are unsure, call. If the answer is teething, great — you wasted a phone call and gained peace of mind. If the answer is something else, you caught it early.
Teething does not explain multi-system symptoms. A baby with a fever, runny nose, and diarrhea does not have "really bad teething." They have an illness affecting multiple systems, and they need evaluation. Teething affects the gums. That is it.
Trust the parent who says "something is off." Research consistently shows that parents who know their babies well are accurate assessors of when their child is genuinely ill. If your gut says this is more than teething, act on that instinct.