I also have Emetophobia, I had one really bad period a while back where I thought I was going to be sick but I noticed its from the pain, now I ensure I take enough painkillers to lower the pain and therefore prevent the possibility. I used to be scared of taking these painkillers in case they reacted with my stomach but now I know it's better to do that than the pain causing nausea. I just want to emphasise, it's only the pain not the period that could make you sick.