Anything is possible, so in that belief, then you can fight panic and anxiety with "mental power" alone.
There are many people who swear by certain literature, some by herbal remedies, some by yoga and some by a combination of these and other natural approaches. And some of us have needed medication.
There is no one "right" way for all of us.
I would suggest you see a doctor to first rule out any medical reasons for your anxiety and perhaps a Naturopathic doctor would be the better choice for you. I applaud your desire to deal with this on a natural level, but sometimes we just need more help and there is no shame in that.
I'm sure there will be many responses from folks who have found natural remedies that have helped them.
Please let us know how you're doing, OK?
Peace
Greenlydia