I think you added the fever part, that certainly would have contributed to a more clearly defined dx of sepsis. The findings given aren't necessarily specific to sepsis, and most could also be explained by aseptic decompensated heart failure. Although it does become a little trivial, since one of the main components of sepsis is circulating negative inotropes, so in the end what you're dealing with is fairly similar.
If Norepi is being given, then it's very important that the patient have sufficient intravascular volume for the Norepi to work, which usually requires a volume status more on the fluid overloaded side. Once-upon-a-time, Norephinephrine, ie levophed, was referred to as "leave-'em-dead" since it wasn't found to be all that effective, until it became more commonly understood that Norepi doesn't do much in a hypovolemic or even normovolemic patient. So to diurese a patient on Norepi would mean the patient would have to have so much excessive intravascular volume that diuresing would still leave them somewhat fluid overloaded, the only obvious indication for that would be fulminant pulmonary edema, otherwise you're going to need that fluid volume to stay in there for the time being. It may also have been that the patient was hyperkalemic, in which case lasix would be a good option but may requiring replacing the diuresed volume with IV fluids.
A better option for dealing with fluid overload in this patient would be to look at cardiac output vs metabolic demand, either directly or by indirect indicators like an ScVO2, and give an inotrope if indicated, if that works sufficiently then the kidneys will get rid of that extra fluid volume when they deem it appropriate.