I'm confused, sorry. When you said that you had a false positive, do you mean that the test was positive when you weren't actually pregnant? The reason I ask is because that is highly unlikely as hpts are very rarely falsely positive, but more often falsely negative. If you had a positive test and are now testing negative I would say you likely had a chemical pregnancy.
However, if I misunderstood you, please correct me. But, if you had a chemical this means that you are indeed fertile and were pregnant very briefly.
If you are TTC I would start tracking your cycles to try to find out when you are most fertile so you can hopefully speed up the TTC process. Sign up for Fertility Friend. It has great tutorials and info on learning how to chart.
Good luck!