I think there are variations of rapid cycling, in my case I don't cycle so much in a day but I can in a week and most definitely over months. I've already had a 2 month episode of hypomania which morphed into a mixed episode for a month which then morphed into 2 months of depression fueled by high levels of anxiety just this year, and my fall cycle hasn't hit yet. That was while taking medicine. I am now on 6 different meds to calm the beast since April of this year. I'm hoping I won't have a fall cycle this year.
Usually I get hyper and have hypomania in the spring followed by a depression, then I'm pretty good all summer, then I deal with depression and mixed moods until the following spring. I haven't been full blown manic since 2010 which was followed by a mixed mood that morphed into a depression fueled by anxiety. That earned me a stay at the psych hospital for 2 weeks. That is how it is for me.

Honestly though, the only person who can really answer if you have rapid cycling bipolar or something else is your pdoc. Ask the hard questions, be an informed consumer.