Why would your doctor run a test 9 days after possible conception? That doesn't make sense to me. The second test was within the time frame that you should have gotten a positive if you are pregnant.
What further testing has the doctor suggested since he says it sounds like you are pregnant? Blood test? Ultrasound? These are all tests that should be done if he truly believes in your symptoms being related to pregnancy.
That said, the same hormones that cause pregnancy tests to be positive are the same hormones that cause symptoms. If you have enough hormones to cause all those symptoms, you have enough hormones to trigger a positive pregnancy test.
Symptoms do not indicate pregnancy and generally don't begin until your period is due.