I experience anxiety and panic pretty regularly. There are a handful of things I do to deal with it that are inadvisable (primarily that I do a lot of retail therapy despite being broke most of the time), but a handful of things I do that I would recommend include:
1. Meditation. I find that for me, panic and anxiety are usually rooted in not being present: I'm either ruminating on the past, or terrified about the future. I'm not sure if it's the same for you, but try asking yourself: are most of the things that send you into anxiety or panic things that are actually happening right now, or is it fear of the future or past that sets you off? Because if it isn't about what's going on in the moment, but the past or the future, a mindfulness practice is so essential. Mindfulness doesn't have to be meditation, but meditation is a really good one. If the idea of meditating in complete silence sounds difficult to you, try looking up guided meditations or meditation music tracks on websites like YouTube, it gives you something to focus on while still allowing you to be present and mindful. There are other ways to be mindful as well though, including body scans (mentally going through a checklist of different parts of your body and relaxing them, one by one, usually starting at the head and then going down the face, the neck, shoulders, arms, torso, legs, and then feet), eating a group of small foods (like candies or nuts) and eating them one at a time and really trying to mentally think about all the qualities of the food (is it chewy? crunchy? sweet? salty? sour?), and probably a lot more.
2. Fidget objects. I'm personally on the Autism spectrum and usually only see other Autistic people or people with ADHD talk about these being necessary for mental health, but I thought I'd bring it up anyways. Sometimes, I find it's way easier to go through stressful situations when I have something to do with my hands. I have this ball that is full of a foam that makes squeezing it feel weirdly similar to chewing gum, and any time I have a doctors appointment, I bring it with me, because I find it easier to talk when I have something to do with my hands. Having an activity to do helps me stay grounded, while also managing to help me divert some stress feelings into fidget feelings.
3. Consider your habits. There are some things people do that can increase their anxiety from a physical way. For example, if you drink a lot of coffee, or don't sleep enough, or intentionally do things that trigger anxiety more often than you need to (an example is looking at drama websites or not limiting your time reading about political and social issues). Are there any habits you have that might contribute to anxiety?
4. Make sure you have an outlet for your feelings. Do you journal? Do you have any creative outlets where you can express your panic and anxiety? Do you go to therapy, or do you have any friends you feel comfortable talking about your anxiety to?
4.5. Really emphasizing that, if it's available to you, therapy is seriously a good idea. Even if you feel embarrassed, or maybe feel like you aren't unhealthy enough to need it, there is nothing embarrassing about needing therapy, and even mentally healthy people should consider therapy to keep themselves healthy- sort of like how people go to a medical doctor for a check-up even when they aren't sick.
5. Music. I find music can be really good for working through your feelings. That being said, I think you should think a lot about what kind of music actually makes you feel better. I went through a phase where I listened to angsty music because I related to it and I thought that made me feel better, when in reality, I was just wallowing, and I've become a lot happier since I've switched to listening to more cheerful music. Not saying my way is best, for some people, I think the angsty music does really work. But if you aren't sure what works best for you, maybe make different playlists that have different moods (sad, happy, angry, etc) and then try journalling about your feelings while listening to the playlists to see which ones actually make you feel better.
6. Get a hobby. The times in my life that my anxiety is the worst is when I'm not invested in anything. Having something you love so much that it fills your thoughts can really help get rid of anxiety feelings.
7. Consider getting a pet if you are allowed. This is probably something you've already considered, but if you are allowed to have pets in your building, aren't allergic to them, etc, definitely consider getting one. Cats are probably one of the easier types of pets to take care of (don't be fooled by pet stores trying to trick you into thinking fish or rodents are super easy to take care of, a lot of pet stores sell smaller cages/tanks than are actually healthy for animals to try to sell the idea that they're "convenient pets"). It's scientifically proven that having a pet can decrease stress levels. If you already do have a pet, maybe try to schedule more time playing with them or snuggling with them even more, to really just soak up the benefits, along with making your pet happier with the extra attention.
8. As others have said, aromatherapy can help. Personally, something that helped me a lot are essential oils that can be applied to the wrists, and can be inhaled. Really strong smells can just totally bring you to another place. Candles work too, but they aren't quite as portable, nor as intense, in my personal experience. That being said, if you do decide to take my advice, definitely do research before you buy the oils, as not all oils are meant to go on the skin, and even the ones that do go on skin, usually you want to check the label for certain levels of purity or certain concentrations- despite essential oils sometimes being portrayed as 100% safe because they are all-natural, sometimes they can be made using plants that are poisonous, or poisonous in certain quantities, even when just applied to the skin rather than ingested, so you really wanna research each individual type of oil. It mostly depends on what you plan to do with the oils, along with what the oils are actually made out of, all plants are different so it really is an individual thing.
9. Really intense tasting food can help too. Definitely see what works best for you, as I could imagine something like that could potentially cause sensory overload and cause more anxiety, but I find intense sensory experiences often take me away from my nervous thoughts. Something like extremely sour candies, or really spicy food. Gum can also help the way that fidget items can, but are a little more nonchalant than a fidget toy.
10. Keep your room clean. I find that visual clutter can make my anxiety go from 1 to 100 so fast. Having a space you keep clean and can really relax in can really help. If your room is super messy and the idea of cleaning it stresses you out, just try to make a small dent every few days instead of having a huge cleaning day, and try not to have habits that will re-mess it (like leaving mugs around after you finish drinking from them). Rather than saying "by the end of the day, I'll have my room clean", every few days, I'll just set a timer for 15 minutes, and just clean my room however I can until the timer runs out.
Those are the top 10 tips I could think of, hope that wasn't too overwhelming!