What are alternative ways besides medication to deal with the physical symptoms of anxiety?

Exercise most definitely. Its a natural stress relieving mood booster. Even a 10 minute walk in the fresh air daily will help reduce anxiety.

Ways to personally cope with anxiety vary from person to person, I recommend trying things that are calming and soothing that interest you. I find that talking to mellow, older adults is very soothing. I also exercise, listen to anxiety related music, tend to my garden, and cook warm foods to calm down after a panic attack. It stops the shaking.

Yoga, meditation, some natural herbs, teas, reiki, therapy, mindfullness, excercising regularly, hugging (yes, really), loving.

Often times, thinking about calming yourself down when you are anxious only makes it worse. A helpful trick I have learned is tricking yourself into thinking that you aren't actually anxious, curbing mental anxiety and therefore the physical symptoms. For example, if you are anxious about presenting a project in front of a class, be happy about it. Never admit that you are nervous, and you won't be. Trust me, it works. Acting confident makes you confident.

I go on walks or listen to music or play ukulele or piano when I get anxious, I also sometimes read, drink a warm drink or wrap up in a blanket to feel safe.

Deep breaths. I know it sounds silly but it's the oldest way to help and it really works. Try to focus on one single thing, it helps to have a distraction. Focus on your breathing and the way your muscles feel, and try to relax them.

There are several ways which can help you with your anxiety, so you may want to try them out to find the one which is the most suitable for you. For example, some people feel a lot better when they excercise. Moving your body helps you not only burn some calories, but your brain distributes some hormones of "happiness" afterwards, so you feel a lot better than before. If you excercise in nature, you also gain more oxygen, so that's really great as well. When talking about oxygen - try taking deep breaths. Find at least several minutes in your busy schedule and stop doing whatever you're doing, and focus on your breath. Breathe deeply, fully in, fully out, feel the air filling your lungs.. it may seem a bit silly, but it really does help. It also helps when you're really stressed. Relaxing music helps a lot, too. Try playing some on youtube, and just relax. You can listen to instrumental music, sounds of nature (rain, storm, birds singing..), anything you like. Other things I recommend are - doing something creative (drawing, sculpting, ...), eating healthy food (fruits, vegetables) and drinking a lot of water, drinking (herbal) tea, maybe aromatherapy or yoga, etc.

I use physical activity such as walking or yoga. Meditation and certain breathing techniques really help!

Calming down your breathing and counting out your breaths. Or holding onto something and running your hands across to help ground yourself.

Homeopathy, but I find mindfulness very helpful. Thinking on your senses during an anxiety attack. Maybe do a panic bag with things of your senses. Mints, lavender, crunchy noise, marbles.