Is it possible that I haven't developed an immunity to mono? Third time.?

A couple of days ago I woke up with a full-fledged throat infection. (Red, almost purple throat, enflamed tonsils/glands, white patches on the tonsils etc.) A day later I started feeling the all-too familiar extreme fatigue and abdominal discomfort. I went to a walk-in clinic today and the doctor took a throat culture. He said it was probably strep, but could also be mono. I said I'd already had it in grade five. When I recounted this to my mother later, she was quick to remind me that I also had it as an infant. Which leads me to my question; If I've had it twice before, is it possible to get it a third time? Does that mean I don't have an immunity to it? Anywho, the doctor didn't poke around to see if my spleen was inflamed either.