Ignore the dates on a home test, they don't mean anything, as your doctor said. They are an ESTIMATE based upon the level of hCG, the pregnancy hormone. It varies and is not a reliable indicator of how far along you are.
Timing starts on the day your last period started. We don't base how far along you are on when you conceived as that varies.
As to your question, from your description it is unlikely that you are still pregnant. You likely had a miscarriage. They are VERY common early, more so than most women believe.
It is early for an ultrasound. Just finding the sac can be a challenge. Waiting another few days to a week improves the results.
A home test would still indicate pregnant, either way. It takes time for the hCG levels to drop.
Good luck. Hope it helps.