I like to think of myself as a kind of panic expert. I have depression and anxiety (I was diagnosed as a teenager) and the result is that I live with high amounts of stress no matter what's going on around me. So I'm familiar with a good amount of coping methods for dealing with stress, most of which were learned in therapy and by talking to other people, and also just through personal experience. These methods are largely applicable to panic attacks, too, which I know many students deal with, no brain issues required. The building pressure of deadlines and classes and the weight of carrying your whole future on your back can do that to anybody. So, when it feels like the world is ending, here are some coping methods that can hopefully help.
First, find somewhere to be alone for a minute. This one is based on personal experience more than anything else. When I'm really panicking, I just need somewhere private to collect myself and remember that I'm not actually going to die. If you're with a group of friends or in class and aren't able to explain the situation, just say you really need the bathroom. Once you're a little better, I'd try reaching out to someone that can help calm you down some more.
Try to focus on what's around you. This one is especially good if you're not in a situation where you can just get up and go somewhere private to collect yourself. It's technically a self-grounding technique, but it works just as well for panic attacks. Look around and focus on just one thing at a time, deliberately and meticulously describing that object to yourself. This works as a distraction and also as something that can reorient your brain when it seems like everything is crashing around you.
Everyone's heard this one, but it really does work. Take super deep breaths, in through the nose and then out the mouth. It'll slow your heart rate and will help relax you, even if just a tiny amount.
Once you're out of the situation or you're in a place where you can just be by yourself for a little bit, put on your favorite quiet or soothing music. I personally keep a couple calming playlists prepared for this kind of thing. Just like deep breaths, this is intuitive and obvious, but it's easy to just sit there in increasingly-stressed silence and forget that you have ways to help yourself.
If you still can't stop overthinking about whatever situation led to the panic attack or increased stress, just write down everything and anything. They don't even have to be real or full sentences, just get all the words and thoughts out. Throw it away or delete it afterward if you want. It's your choice.
These are just a couple methods for helping with a panic attack or extreme stress, but they're the ones I either personally use or have had recommended to me by friends. Please comment if there's something different that you use!