What is the best way to deal with anxiety w/o meds, and could this be genetic or sleepness related?

As above . Mood symptoms can be inhireted in addition medical condition , increased stress level , substance abuse can contribute to mood symptoms ( depression and anxiety). Exersize and cognitive behavioral therapy can help.
Try mental focusing. Anxiety is tough for many people. Meditation can help in some people, for it helps calm them and trains their mental focusing ability to relieve the anxiety. Relaxations techniques can also be helpful. Maintaining a positive attitude is also helpful. The cause of the anxiety must be discovered and addressed. Sometimes, this latter action is all that's needed.