Is it normal to have bipolar disorder and have a crazy number of mood swings?

I know that seems like a dumb questions, but if I explained the exact situation the title would've been too long. Here's the thing: I was diagnosed with bipolar disorder when I was 16. At that time, I'd been in a deep depression for about 8 months, which was triggered by a random, quite insignificant incident. After the diagnosis, I started medication for it and mostly got it under control once I got used to it and the medication was up to the dose right for me. However, it's been bothering me that A. I don't know what type of it I have because B. I don't seem to meet the criteria for any of them. Even rapid-cycling (in which you have 4 or more cycles of depression and mania a year) is much fewer than I have. I have dozens a month, and it's not uncommon for me to have several a week and recently I've had both a depressive and happy (not quite manic) episode every day (though I'm thinking that's because of my new medication). And the swings can be extreme too--I will go from being content and serene to miserable and angry like a light switch. I will go from considering my mom my best friend to wondering if I really love her because of the bitterness I feel for some of her actions/traits within seconds. There is no in-between for me. It's kinda like PMS or pregnancy hormones, but I'm not pregnant and it doesn't go away. It could be my medication I guess. It's hard to say. I can't remember what I was like mood-wise before this--if I was having outbursts, depression, and really manic days regularly or if I had an episode that lasted for a really long time, with the occasional break (for example, a random fight during a period in which I was on a mental high and loved life). Is this normal for any type of bipolar disorder, and if not, what else could it be? I also have ADHD (and am on medication), and that might contribute to how high I get during the manic episodes.