When people talk about the problem of anxiety (or guilt, or debt, or mistakes) both ridden and riddled show up. The words are close enough to each other in both meaning and form to suggest that at some point in their histories, one of them got confused for the other. So what are those histories? Which is correct?
They both go back a long way. This use of ridden began as the past participle of to ride. In the 1500s you could talk about a ridden horse, and that eventually carried over to the figurative idea of ridden as being affected or burdened by something. The first citation of a compound with ridden in the OED is from 1640: “you devil-ridden witch you.” Many subsequent uses maintained this idea of the “rider” having some oppressive power over the ridden—"tyrant-ridden" (1848), "capitalist-ridden" (1844), "bureaucracy-ridden" (1861)—but it was also extended to anything generally burdensome: "theory-ridden" (1835), "bird-ridden" (1835), "fog-ridden" (1885), "gout-ridden" (1901). The sense expanded from “having an oppressive thing metaphorically riding on your back” to “beset by something annoying.”
While ridden goes back to a familiar verb form of ride, riddle is not related to the familiar word we know for “enigmatic question.” It’s from a different word, an Old English word for "sieve." A riddle was used to sift gravel or ashes, and by the 1500s riddled had become a way to evoke something sieve-like or filled with holes. It showed up in the descriptions of post-battle scenes where the effects of ammunition could be seen on things like “riddled ships” and “riddled flags.” Compounds with riddled started in the 1800s, first with "shot-riddled walls" (1836), then “rat-riddled stairs” (1855) and “worm-riddled rafters” (1893). It wasn’t long before things were bog-riddled, cliché-riddled, traffic-riddled, or allergy-riddled. The sense expanded from “full of holes caused by X” to “afflicted with X.”
Both ridden and riddled ended up meaning “afflicted with” or “beset by” but through different metaphorical paths, one with the imagery of a weighty burden, and the other with the imagery of being punched through with holes. There may be faint echoes of those different images when we judge whether a given use sounds better with one or the other today, but the choice seems to be mostly governed by grammatical structure. To my ear, ridden simply sounds better in a compound ("anxiety-ridden"), but riddled sounds better in a phrase ("riddled with anxiety"). Google hit counts back me up on that: the ratio of anxiety-ridden to anxiety-riddled is 71:7, while the ratio of “ridden with anxiety” to “riddled with anxiety” is 7:32.
In any case, both are correct, so don’t let anxiety over the ridden/riddled question weigh on you too heavily or pierce you too much.