Faking a miscarriage?

My boyfriend and I suffered a miscarriage back in May and only very recently (late August)  told our family about it. Thinking about it, remembering it, wondering what could’ve been kills me. One of the people that we told was my cousin. We are four months apart in age, grew up like sisters and have been in competition over everything our entire lives. A week before we told her we were pregnant she told us she was getting her tubes tied. After we told her about our miscarriage she told us she was no longer getting her tubs tied. Now a month later she calls to say she had unprotected sex then 2 1/2 weeks later she’s had a miscarriage. When telling me the story there was no emotion there was no heartbreak, there was no sadness, she even smiled while she told it. Every part of me is convinced that she is lying. My question is is it even possible to conceive a child and miscarry that quickly? I’m just so beyond upset by this and I feel like it’s going to be the end of our relationship.