Dreams do not break celibacy. However these dreams could be caused due to you keep thinking about sexual acts, watching tv shows, dramas arousing such thoughts etc. during the day while you are awake. In any case, merely keeping to the precepts is not enough. You have to guard your mind as well. I would suggest practicing Patikulamanasikara meditation as a supplementary meditation in addition to the mindfulness meditation.
Also, before you go to sleep, chant the Nine virtues of the Buddha. After that, practice mindfulness while lying on the bed and let yourself fall asleep naturally instead of trying to sleep.