All the web hits for 'innerliche Unruhe' are in a psychological context, which would be something like (internal) agitation, restlessness, disquiet, unease.
Unrest, in contrast, is usually discontent in a public sense, an unsettled political environment. Bad conditions for people in a group, like a school or office, could lead to a general feeling of unrest. And 'internal unrest' is often a euphemistic term for public disturbances within a country: rioting in the streets, skirmishes a few levels short of actual civil war.
'Inner unrest' doesn't sound familiar to me at all. Maybe there's some context I'm not thinking of, but with no context at all given, I can only go on what seem to be the usual meanings of the words.