Dictionary definitions define the three words:
in a way that they carry almost exactly the same meaning (at least to me as a non-native).
The only difference between “deteriorate” and “aggravate” is that, “aggravate” is transitive, while "deteriorate" is an intransitive verb.
Now, in order to identify the slight nuance between them, I have made two examples; please kindly let me know about the correct / incorrect choices in each example:
The US government officially threatened North Korea last night. I think the political situation is ____________ for them.
c. being aggravated
The three options are the same to me here and work properly.
The noise ___________ my headache.
Here, I think both words are identical.
I don't know how a native would interpret them.