I didn't pay attention to that twinge of (a) thought of losing what I hadn't lost yet.
Should there be an article in this phrase?
I would say yes, it needs an article.
A 'twinge' is a sudden sharp pain. It is not being used here as a measurement of thought, like you would say "a moment of time". It is saying that the thought was like a twinge, that it occurred suddenly and sharply. So "a twinge of a thought" is syntactically similar to expressions like "a giant of a man", in which a man is being likened to a giant.
I agree with Astralbee that an article is needed, but I am surprised nobody has mentioned the definite article. The definite article would sound better in this context
I didn't pay attention to that twinge of the thought of losing what I hadn't lost yet.