We've been dealing with this a lot with tylenol for teething! (hintmama.com)
I am so thankful for TYLENOL ® PM at Walgreens, because I can get a good night's rest for a full day ahead. (curlycraftymom.com)
As for your two «rules of medicine» I have to assume that you never take or give tylenol or ibuprofen to your children for fever or pain, as both of these are signs that the body is working as programmed (fever increases blood circulation to more quickly distribute antibodies, and pain to tell us «don't do that»). (religion.blogs.cnn.com)