Using appositives as stand alone sentences

Ok, first of all, I may be using the wrong terminology by calling them appositives, but from what I understand, that's what they are.

Is it considered grammatically incorrect to do the following:

"She looked like she was suffering from a headache. A great, big, agonisingly painful headache. "

"There was something lurking in the shadows. Something evil."

Here is one famous example that I can think of from classic children literature:

"The Grinch had an idea. An awful idea!"

In all cases, the further description is added as its own standalone sentence for added emphasis. But is this not technically wrong, as the sentences are just appositives and don't have verbs?

Are there any grammatical rules that I do not know of that allow for such examples like this?