Positive test after chemical?

Hi! I got a digital positive test this morning (7/26). I had a chemical pregnancy last month, confirmed by blood test on 6/29 when my hgc was at like a 6 (very low). Do you think it's possible the test is a false positive a month later? Can very low hgc stick around for a month? Don't want to get my hopes up if this is a common misconception.