The whole thing about anxiety is that it's intangible and that's what's scary - you feel like you've lost control of your body (and mind) and that causes fear and panic.
I had panic attacks in my 20's from a build-up of stress, loss of my father, and low self-esteem - seeing others in London making money when I was broke, single and renting a pokey little room. I also suffered a loss of confidence in my body and badly hyperventilated - a kind of panic - after a marathon.
I had no real help at the time (1980's) from doctors - just pills - but I wish I'd had some therapy to help and reassure me. Of course cycling will help, but I'd suggest some cognitive therapy if you can get it.
The good news is it's quite common - in younger men especially - and I 'grew' out of it within a couple of years. Also, since giving up alcohol a few years ago I feel better now than I did 30 years ago... honestly.
Good luck.