It is contrary to Christian teaching to say that "Non-Christians don't have fear of divine vengeance." The first Chapter of Romans clearly states that Non-Christians know of God and his retribution of evil for evil, but repress this knowledge. The unfaithful may try to push the anxieties out of their heads, but they will never go away. Non-Christians like you fear God but try not to. They try to pretend that his retribution does not exist. Look around you at this forum -- the unfaithful here are all trying to assuage their troubled minds!

(Some Non-Christians, for example, Platonic Theists, try to persuade themselves that what they are fearing is a corrective punishment by God. They claim that divine retribution is proper to fear but also proper to experience. But this too is a repression of reality.)

But there will not be peace except for the peace of God on his terms. Let the fear remain until your throw yourself under the aegis of the cross!