Whether a test is positive or not depends highly on what type of test it is, and when you are tested relative to symptom onset. You can absolutely be carrying the COVID virus but still test negative. Heres a paper with a handy chart: https://jamanetwork.com/journals/jama/fullarticle/2765837

I think you testing negative was a combination of the rapid test being unreliable, as well as getting tested early with respect to symptoms.