I have anxiety with mild OCD... in my case there's some skin picking/nail biting/fidgeting but luckily not enough to alter me visibly. I'm more of an internal obsessive... the way some people check door knobs, I'll revisit a conversation or an interaction over and over again if I'm feeling anxious.
Medication is working wonders for me after several years going on and off, but I respect your choice... it's not for everyone.
Have you tried doing yoga regularly? I go to a nice vinyasa class (flow rather than static poses) 5 - 7 days a week and it makes a huge difference in my anxiety levels. When I skip it for a few days in a row I can really feel the difference. And a nice side effect is that it's really good training for impulse control, which has been helping me deal with alcohol cravings and urges to futz with my skin.