There is such a thing as ultra-rapid cycling bipolar and with some mixed States (periods of high and low mood at the same time) where there is a little definition between the two moods. So even though rapid changes of mood aren't classic bipolar symptoms it doesn't necessarily rule it out.
There are a few orher things that can cause mood fluctuations like you describe, it can take a while to work through all the possibilities.
One thing that might be a good idea is to keep a diary of yours moods and what was going on in each mood state. It will help you and your doctor to work through the patterns which can help towards working out what might help you and then what it might be.
There are also physical illnesses that can cause mood irregularities so it might also be worth speaking to a doctor about ruling the out also.
Whilst it can take a while to figure things out that doesn't mean that things can't improve along the way. Good luck!