First and foremost, don't panic! All this does is make you more anxious; no-one can execute any function at their best when they are feeling tense. However, not being anxious doesn't mean to switch off and be lazy. Keep alert but make sure that you have worked the breathing places into the voice just as much as you would the notes, rhythm and words.
Managing breath control comes after preparation, of technique and of a holistic view of the piece. During practice, you will have decided where to place the breaths within the song, and maybe even changed these as you worked through the song over time, and became more proficient as a singer.
A tutor from my younger days told me that I was actually allowed to breathe within a phrase, and in fact that would be preferable to demonstrating that I couldn't sing the whole phrase in one breath comfortably. What is important is to keep the sense of the whole sentence clearly in mind throughout the whole phrase including when the breath is taken, so that you retain the line without interrupting it with a stilted in-breath. Practice saying the words with the breaths at the designated places, as though you were speaking to a class of enthusiastic youngsters and therefore keeping the meaning very clear. The posture should remain upright, allowing the lower abdominals to release and engage rather than working from what will inevitably become a tense throat.
Initially, humming evenly for a set number of counts is a good exercise, and then increasing the counts - by design, not by chance so that you really plan your exhalation. A seasoned singer who knows that the phrase is too long for them to sing in one breath, may use an extra breath as an interpretative tool. By doing this an extra accent or weight on a certain word can enhance the lyric and no-one would know that the sneaky breath has been taken - a glorious "non-cheat".
As you may have read from my first blogs, breathing is fundamental to life and we breathe without worrying (if we have no chronic respiratory problems of course). Endeavour to accommodate your breathing in songs not as an annoyance that hinders your interpretation, but as part of the whole natural flow.