Step 1: Use the gap between infection and kidney disease as the main filter.
Different causes of post infectious hematuria have very different time gaps, so lining up the given 3 day gap against each option quickly narrows the choices.
Step 2: Line up IgA nephropathy first.
IgA nephropathy is famous for the "synpharyngitic" pattern, hematuria appearing at the same time as or within a couple of days of a throat or upper airway infection. A 3 day gap fits this pattern closely.
Step 3: Line up PSGN next.
PSGN needs an immune complex response to build up, so its typical latent period is about 10 to 14 days after pharyngitis, sometimes longer after skin infection. Three days is much too short for PSGN to have developed.
Step 4: Check HSP and HUS for fit.
HSP would usually be recognized by its skin purpura and joint or belly pain alongside the kidney findings, and the case here mentions none of that. HUS is linked to a preceding diarrheal illness rather than a respiratory one, and comes with anemia and low platelets, not just isolated hematuria.
Step 5: Conclude.
Since the gap is short and there is no rash, joint pain, or diarrhea mentioned, IgA nephropathy fits best.
\[ \boxed{\text{IgA nephropathy}} \]