A.H.
Sorry this is going to be really long.
You're right, tantrums are normal. Although she has a lot of words, maybe she's still struggling with trying to communicate with you unsuccessfully - when my son has tantrums (he's 19 months old), that's usually the problem -he thinks I don't understand what he's trying to say. Now if they are tired or hungry (sounds like she was thirsty and tired during that 45 minute marathon, or became that way during her freakout which made everything worse), those things need to taken care of immediately. Otherwise there's no hope with the tantrums, they need those needs met immediately. But if she is changed, fed, rested, and then a tantrum occurs, I've learned a couple of things that have made a WORLD of difference in our household.
1) If you aren't able to stop a tantrum that has come on (and usually you can't), and you are at home, you can stay in view of her if you think she's going to feel abandoned if you walk away, but I wouldn't stay CLOSE. That's feeding too much attention to the tantrum. Really you need to ignore it. It's so hard at first, but once she realizes she's not getting the response she wants, she will realize that it's not working. If you are out in public, move her to a quiet place so she can calm down without making everyone else around you miserable (not that I care all that much what people think, but I am respectful when it's possible). As long as she's not going to hurt herself, IGNORE it. It will start to work. Trying to figure out what she wants in the middle of the tantrum is an exercise in futility AND teaches her that a tantrum is an effective way of communicating with you. You will be helping her by ignoring that behavior so her real communication skills can be developed. Also I always have something to drink out for my little one...he's so thirsty all the time, and it keeps him well hydrated. One more thing on this - try the book Baby Meal Signs, it teaches sign language for basic baby foods so she can ask for them without knowing the actual words yet. My son learned them in a month when he was 14 months old, and communication has not been his strong point. So she would probably learn them even faster.
2. Ok, through a few months of worrying about having a tantrum kid and wondering how in the world we will ever get through the terrible 2's, I stumbled upon this wisdom. Dr. Karp, the guy who wrote Happiest Baby on the Block, wrote a 'sequel,' Happiest Toddler. I haven't read this book because it got not so great reviews from what I've seen overall. Apparently it's really repetive and says that toddlers are basically neaderthals and that parents should talk to them as such. HOWEVER, after reading a lot about it online, I figured there might be a little truth to it. The basic premise is trying to be the voice for your toddler. They get so irritated when they want to, say, go outside and play, and we are telling them something else, like they need to get their shoes on first. So the idea is that when you start hearing the uh-uh-uh and pointing outside, that you kind of say what they are thinking - like "Jane wants to go outside, outside!! I understand what you are telling me, Jane, and after we put your shoes on, we're going to go Outside!" It sounds kind of stupid, but I tell you, I tried it on my son for the first time when I was trying to put him into his car seat one day and he did the back arch thing, not wanting to get in. I said "oh no! Charlie doesn't want to get into his car seat, oh no! But we need to be in our car seats to ride in the car." He totally stopped and looked at me, chilled out, and we were on our way.
Anyway, there's no magical 5 S's for toddlers like there are for babies, but these things have worked for me. We are virtually tantrum free now, and it hardly took any time at all. I think no matter what the exact approach is, the important things are patience, warmth, taking the time to treat them like a person, and making your house fun and safe to live in.
Best of luck to you.