Can you catch the Flu back to back?

I received a flu shot at the beginning of October and promptly caught the flu, which lasted 3 weeks. Now it's the first week in November and I'm feeling fluish again with achy neck muscles that seem to radiate down my left leg at times. I'm tired despite sleeping well, and chilled occasionally. My head feels very heavy. The headache I had earlier has faded. My mom and daughter have caught my earlier sickness, but I feel like although I've gotten over the initial flu, I've caught theirs. Is this possible?