I have had this happen several times. I had one child who was rather sickly as a toddler and preschooler and his temp got as high as 106 when he had a bad case of pneumonia. Now THAT was scary!! I hate going to the ER. Half the time they misdiagnose and give your child unnecessary antibiotics. My kids have been diagnosed with ear infections that aren't there when they see the regular doc the next day! It seems like small children never get terribly sick while the doctor is in the office. They almost always wait till Friday evening!
Oh, and I also have experienced the other half of your dream! Fell down a flight of stairs with my 3 week old baby in my arms! Fortunately I fell on my backside while going down the stairs and basically slid the whole way down. Ouch!!!