I'm glad we've all helped you put your mind at ease.
I used to get positives on ovulation sticks but never get a period. I don't know the exact reason why they would come up positive but I just figured it was because my ovaries had started the process of producing eggs but never released them. Your hormones still peak, but they just stop too early which is why the eggs don't pop.
It is hard without a support network. DH and I decided not to tell anyone because we wanted to surprise them with a preg announcement but unfortunately with his fertility issues too we had to go IVF, so after about two years of dealing with it on our own we let those closest to us know our situation. It was such a relief to have people to talk to.
If you get a good gyno or fertility specialist they can suggest someone for you to talk to if you need it. Just so you know the most support I EVER got was from bubhub. I found that even though my family and friends sympathised, they never liked to talk much about it. And I found out after my positive, some of them told me that they were uncomfortable talking about it.
Have a look through bubhub and you can find support groups near you. Some of them even do meet ups. I've met with the IVF ladies in Brisbane before and it was great to talk to people who know what it feels like.