Saying I need pampers makes me look bad in public.
Fighting with your brother in public and throwing ketchup around made her look bad in public - have you considered that?
For the record, my brother started this fight, not me.
Firstly, that is impossible to judge responsibly based solely on your own account. We should hear your brother's version of the story as well (and probably your mom's too) in order to have a better understanding of what actually happened. And it is not even enough to know what happened that day - we should know a lot of your family background and past too, back to several years, to get the full picture.
Secondly, it doesn't really matter who started it. You aren't an automaton who must act in a deterministic manner every time when receiving the same input. You are a human being, free to consider your choices, and their possible outcomes, before acting upon a stimulus. Use that power - that's what makes you human. Otherwise, other people (including your younger brother) can basically control you: they learn that whenever they insult or provoke you in specific ways, you are bound to react predictably, out of anger. And you can rest assured that they will use this knowledge whenever they benefit from it, or whenever they are simply bored and want to have some fun.
I used to be like that as a teenager and well into my twenties. I have an elder brother, and later I had a coworker, who was a genius in pissing other people off. And he did practice a lot on everyone in our team, but maybe most of all on me. After a while, I started to feel as if there was a big fat red button on my forehead with the text "Showtime!" on it, and my coworker, whenever he was feeling depressed or bored, just came and pushed it, then watched the show grinning... it was a very bad feeling. So I decided to defuse that button, and eventually I succeeded, first to make it smaller... then gradually slow and minimize its effects... by now, I managed to remove it almost completely. I still act out of anger sometimes, but very rarely, and even then I can control myself so that I won't hurt or embarrass other people.
It is not easy to learn how to stay calm and not react out of anger in such a situation. It takes years of practice and effort. But ultimately, you will benefit from it immensely - and so everyone else around you. In the short term, your iPod and cell phone may not be confiscated next time - in the long term, you will become a fuller, happier person. I can tell you from personal experience this is worth the effort.
One more thing: the very few occasions when I get angry are almost always triggered by my children nowadays. Raising children is a tremendous - and bloody difficult - test on controlling our anger, among others. I think all of us parents have had some bad moments when we lost our temper, and later regretted that. Including, most probably, your mom too. Yes, shouting at you in public was most likely an uncontrolled outburst of anger and frustration from her part. And yes, she probably regrets it by now, but feels helpless and out of ideas how to influence you and your brother for the better. And yes, she would most probably benefit from practicing anger management as well as you. You may want to talk to her about this - but only after - not instead of - committing to make some progress in it yourself.