Viral infections are common due to their virtually non existent immune system. They get every, bug, virus and everything else when they start nursery. If her vitals were all fine at the doctors try and be reassured. You could give her calpol or ibuprofen for the teething pain and cold teething toys to chew on. Mine likes chewing on cold celery sticks. Cold like symptoms also seem to be common with teething. Just keep an eye on her and make sure she has plenty of fluids and cuddles x
May add she’s also cutting two teeth at once and is screaming in pain with that and frantically chewing on hands