Apparently it's called oscillopsia, and I get it a couple times every year. Usually for me, it wears off after awhile and vanishes for the better part of a year. For me, it usually comes with a bit of ringing in my ears, but I'm not really a doctor (dangit, Jim, I'm a game design student, not an optometrist!), so I can't say for sure, except that for me, it doesn't seem like it's worthy of being upset about, though it is still surprising and startling. I hope that helps!
I get the same symptoms especially when I wake up in the morning my vision is shaking and my peripherial vision shakes all day. Its really bad and gives me super bad anxiety. I feel hopeless....
I also experience things seeming to shake and I also have a lot of anxiety (My actual diagnosis is not anxiety, but bipolar. Oddly, I get really depressed on bipolar meds.), so there may or may not be a connection between anxiety and things seeming to shake. I notice that repeating patterns shake more than anything else. Lines also shake. I went to an ophthamologist and neurologist and both said there's nothing wrong with my eyes and my brain. Before I started taking the vitamin Choline (for my memory), lines used to appear to wiggle, so choline has helped (but not eliminated) the shaking line thing. Choline also improved my anxiety symptoms. I also notice that if I look at random patterns (like popcorn ceilings), they seem to undulate if I relax. I just try to avoid looking at patterns that cause this, since I don't want to encourage it. Just know that there are other people out there like you. I think this whole thing is caused by atypical muscarinic receptors (for the neurotransmitter acetylcholine) since I experienced wiggling lines the first--and ONLY--occasion I ever tried psychadelic mushrooms. I must be super-sensitive, since my husband was pissed off that the mushrooms didn't affect him at all and, since he had messed around with that stuff before, he felt that they had been duds. (I'm glad I didn't try the "good" stuff!) So, since you seem to be a freak like me, don't mess around with illegal drugs! I've been on Lamictal, which eliminates the shaking lines, but it makes me depressed so it's not worth it for me. Geodon and Depakote together make it much, much worse. Take care!
I am not sure this is related to your anxiety. See an ophthalmologist.
Dr. O.