"Life sometimes like a zebra: black and white stripes one after another" —
it's one way of saying pretty common idea that "life is up and down".
«Жизнь как зебра: белая полоса, чёрная полоса, и в конце задница», «Не переживай, скоро и у тебя будет светлая полоса», and many other ways of putting «жизнь» and «полоса/полосочка» in one sentence — it's usually related to that metaphor with a zebra, so indeed, «жизнь в полосочку» is "life is up and down".
The second one is a pretty interesting wording even for a native speaker.
"Небо в клеточку" relates to a prison (windows grills), and probably could shrink to just "в клеточку".
So I believe «через полосочку в клеточку» it's combination of two idioms above about a zebra and a prison — "after a next turn in my life, it's going to be very bad".
Someone with an anxiety could say that, or as motto for not to be carefree.