English Translation
It was sink or swim with me.
Great free translation!
FYI: We usually spell the phrase in Hiragana, but the Kanji is 伸るか反るか. We hardly pronounce 伸る as のる, and 伸びる（のびる）is the standard verb. Some native speakers misspell it as 乗るか反るか, but it’s a common mistake.
Here is the etymology. Arrow makers used to use bamboo trees, which are supposed to be straight so that an arrow strikes at the target. 伸びる or 伸る means “bamboo trees grow up so straight”. And 反る means “they are warped (and thereby useless)”. No one knows bamboo trees will be straight or not. So, 伸るか反るか means “sink or swim” in English.