Disease and vaccine certainly do confer immunity, however, three weeks in between may not be sufficient according to the manufacturer. Since actual H1N1 typing is very difficult to obtain, it is possible to confuse some Rhioviruses with flu.
I would ask your doctor's opinion.
Wayne Yankus, MD, FAAP
expert panelist: pediatrics
Actually, the doctor we took him too confirmed that it was Influenza A, and that the H1N1 was the only one circulating in our area. I have asked this question to his school nurse as well as his pediatrician. Both times, did not get a definitive answer. I do know that it was the flu & not a cold. I'll keep researching, thank you.