Step 1: Note the key timing clue.
The hematuria starts only 3 days after the URI begins. This short gap between the infection and the kidney symptom is the single most useful clue in this question.
Step 2: Recall the classic timing for IgA nephropathy.
IgA nephropathy (Berger disease) is well known for synpharyngitic hematuria, meaning gross or microscopic hematuria that appears within 1 to 3 days of an upper respiratory or gastrointestinal infection. This happens because IgA immune complexes that were already forming are boosted quickly by the new infection and deposit in the glomerular mesangium.
Step 3: Compare with post-streptococcal glomerulonephritis.
PSGN follows a much longer latent period, usually 10 to 14 days after a streptococcal throat infection or 3 to 6 weeks after a skin infection, because it needs time to build the immune complexes that later deposit in the kidney. A 3 day gap is too short for PSGN.
Step 4: Compare with HSP and HUS.
Henoch-Schonlein purpura is IgA vasculitis and can also follow a URI, but it comes with a purpuric skin rash, joint pain, and abdominal pain, none of which are mentioned here, so it is less likely to be the answer being tested. HUS typically follows a diarrheal illness (often E. coli O157:H7) and presents with the triad of hemolytic anemia, thrombocytopenia, and acute kidney injury, not a plain URI history.
Step 5: Final answer.
The short 3 day gap between URI and hematuria is the textbook pattern for IgA nephropathy.
\[ \boxed{\text{IgA nephropathy}} \]