A high fever is not dangerous. You have already gotten this confirmation from the hospital yet you still don't believe. If you felt this was a dangerous situation, you would have brought your baby to the E.R. long ago and not wasted your time here. I'm a mother to 3 young children and I have a sister who is an R.N. and I can tell you from experience that a high fever is not dangerous but scary to you and I understand your concern. I once was a new mom and an unexplained fever can be scary but I can assure you that it is not dangerous ESPECIALLY because there are no other symptoms.
Your doctor/hospital is absolutely correct in telling you to give Ibuprofen and Acetaminophen simultaneously. Make sure you are giving the correct dosages but follow the instructions for the proper intervals of each drug. I have also found that Ibuprofen is much better at managing a fever faster than acetaminophen but giving them together reduces the fever faster. The point of giving the medication is to make your baby comfortable.
I'm betting your baby has Roseola. It almost always comes on with a very high fever, no other symptoms, the baby eats and drinks fine, diapers are fairly normal though sometimes vomiting and diarrhea can accompany the infection but the high fever is the real key indicator. The fever can and most likely will last for 3-4 days (could be a day longer so don't panic). The fever will come down some with the use of Ibuprofen and Acetaminophen but it will NOT completely go away. Call it a persistent fever but this is indicative to Roseola. Once the fever breaks, a rash will break out over your baby's body. Can be isolated to the tummy but can be spread out over the back, legs and even the neck. The rash will be red and bumpy and will last for maybe 3 days tops and then it too will go away but the fever will be no more once the rash breaks out. It is a harmless infection and is inevitable that every baby will have had this infection before his/her 2nd birthday.
Fevers are not dangerous. I've had more than my share of experiences with fevers and all 3 of my children have had Roseola and I am willing to bet that your baby also has this infection. Google it and read it for yourself. It's harmless.