doctor said it was a chemical pregnancy but ...

Hi there ... so if my pregnancy would have stuck I would have a 1 year old right now . My boyfriend and I were talking about it . We know when we would have conceived and the time frame doesn't make sense for it to have been a chemical pregnancy . We had tons of unprotected sex in April of that year because we went to Mexico ... and then all protected Sex throughout may ... I took a pregnancy test on May 17th and got a Positive and then a ton of negatives and barely a positive blood test . That's when a doctor said I had a chemical pregnancy . I bled a lot, had bad cramps and passed tissue shortly after and it wasn't my period . But from the time that I found out and had a positive test  , it would have been over a month since I would have conceived . Wouldn't it be impossible for it to have been chemical ? Wouldn't it have been a full on miscarriage ?