High fevers in infants can be quite serious, even fatal, so yes you do go to the ER for a high fever in that case.
This old, but I was ridiculed at my ER visit w/ my >1 y.o - after waiting for many hours they mocked us since her temp was only 104.8, not the truly urgent at 105.1, or some such numbers, an arbitrary distinction at least to us non-pediatric physician types. The little thing was clearly in trouble and the creeps had no compassion.