Magic powers aside, we could rephrase your question to:
How can I make my character mad?
The magic powers are a result of anger, so we can ignore the magic for now. (and I know your character also uses magic when scared but Ceramicmrno0b already gave an answer on that)
There are lots of ways to make your character mad. Here are a few:
- Heated debates
- Anger/Grief confusion
- Self Pity
Those are just a few options, but I want to go over why I picked each of them.
Insults: Even the best of us gets angry because of this. No matter the circumstances, we tend to get mad at people who direct insults at us. Whether they are personal attacks, offending jokes, racial slurs, etc, our respect for the other person quickly drops, and we descend into a fit of anger depending on the particular aggression of insult. And for the more hot-headed, this can be particularly infuriating, probably infuriating enough to explode the offending person.
Heated debates: Depending on your character's personality, this could be the root of anger or not a reason for anger at all. Assess your character. Do they strive to be right? Hate being wrong? Talk before thinking? If that is true for your character, then this is a perfect cause of anger. All she has to do is start arguing on a touchy topic with another stubborn character, and boom 10 minutes later it's a shoutfest that leads to your mc's magic powers coming out.
Anger/Grief confusion: Often, when we are disappointed, rejected, miserable, etc we want a scapegoat for our blame. And, even if the scapegoat had nothing to do with the character's grief, she can find a way to point her finger at them. Her aunt died in a car crash? Blame the pedestrian the cab driver swerved to avoid and hit mc's aunt. This is an easy strategy that most of us use in real life to encase others in our misery.
Losing: Some of us climb so hard to be winners in life, when we fall, we fall with hatred and anger. It happens in the big picture and in regular life. You get mad when you lose. You accuse the winner of cheating instead of owning up to your losses. This can fuel the rage that will spark the 'magic powers' in your mc.
Self-Pity: If your character has lost someone, failed to save their friend, or made a mistake, they may get so engulfed in self-pity that they envoke their magic powers.
Use these 5 tips as a starting point, but there are many more out there. Make sure the strategies that you use to get your character mad matches up with their personality. Keep in mind: while your mc uses magic, they should still seem human when reacting to situations.
Model your mc's complex emotions off of someone you know, or yourself to ensure that the mc will rub off like a normal person reacting to normal scenarios.
An interesting idea would be to arc the character's control to a point where they can chose when they use their powers. Controlling ones anger is an important thing in life.