Teething = infections?

So my girl only has 2 teeth so far, can up a few months ago and when they did she also got a fever and ear infection. Teething again now for a couple weeks and got a fever 2 days ago so we figured, teeth are serious and will be up in a couple days. Well ended up taking her to emergency last night cuz her fever spiked and was puking, shaking and lethargic along with all the screaming. Dr figured she has a throat infection and prescribed antibiotics. shes a lot better today, still sick and unhappy but shes got some energy back at least.

Anyway, is it common for them to get this sick every time they teeth? Shes a healthy baby, and we haven't been around any kids in the last week so I dont think she could have caught it from anyone.. Just wonder if we have this to look forward to every time she gets a tooth