Figurative meaning of в полосочку

"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".

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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.

There's a saying небо в клеточку, друзья в полосочку ("checkered skies, striped friends") which is a metaphor for prison. This refers to the windows grills and prison uniforms.

There's another, unrelated idiom черная полоса, literally "black stripe" or "black streak" which means "a rough patch" (in someone's life), and its opposite белая полоса (literally "white stripe").

It's hard to say for sure without context what exactly do your sentences mean, and I've never heard them in the very form you're quoting them, but I'd think they allude to one of these metaphors.