Nocturne, Horrifying ability says that you can play him when you look at cards and don't draw them. Does that mean when I play Trifarian Captain, I can't draw after playing Nocturne?

Yes — you still draw. Trifarian Captain's look and reveal-and-draw are all one resolving effect: seeing Nocturne among the top 4 just lets you banish him and pay [A] to play him right then, and the effect continues normally — reveal a qualifying unit/gear (Energy ≤ [3], Power ≤ [A]) and draw it, recycle the rest. Nocturne finalizes onto the board once that whole effect finishes (FAQ #12292), so nothing about the draw gets cut off.

Worth correcting the premise: "(and don't draw them)" is Nocturne's old printed wording. The 2025-10-21 errata changed him to "As you look at or reveal me from the top of your deck, you may banish me…" — so it's look or reveal, with no "didn't draw" condition. And since Nocturne is 4 Energy, he never meets Trifarian Captain's "Energy cost no more than [3]" restriction anyway, so he was never a card you could have drawn off the Captain.