Is BBT accurate prediction?

I know bbt can be an accurate way of predicting ovulation when you get regular sleep and take your temp the same time upon rising every morning. But what about a nursing mom who nurses throughout the night? I’m up at different times (bedsharing and nursing) and we don’t wake at the same time every morning. Would a bbt be accurate? I just started menstruating again after 15 months of breastfeeding. Still nursing but now ovulating too. We don’t want to get pregnant right away but I also don’t want to take birth control while nursing. How accurate is bbt in this situation. Any experiences welcome.