When I first read this I thought you were going into a market that was way too crowded for you ever to succeed (in English at least). But actually the top search results for "track menstrual cycle" and "track period" and several other searches are not that strong and with the right SEO you should be able to break into the top results. The landing pages of your competitors are awful. Too much text and too much of it in light pink which is hard to read. A simple high impact landing page could help you beat a lot of your competitors - but that isn't going to help if you cannot drive people to your site with the right SEO.
Two other ideas for you to think about. 1. what is the market like for other languages? Maybe there is a lack of Spanish language competitors etc - it might be easier to get going with them first. 2. I don't know if you can create a widget that can be included on forums, but there are a lot of womens forums around where they discuss all sorts of things. A lot of these women are trying to get pregnant and if you can tap into them on those forums it could be a good marketing opportunity.
Obviously as everyone else has said here, do get the English right, and it could be worth checking if someone in a foreign country uses the site and for some reason feels they want to sue you that you are safe.
Good luck.