You failed a drug test where? Doctors only have access to your health information -- they aren't really all that interested in even that. Ever seen a doc who has truly thoroughly checked your health history?
It's possible depending on what database your records are entered in and where you took the test. The ACA (Obamacare) brought sweeping changes to electronic records - keeping laws as well as insurance.
Right now there is not a national, shared medical records database, but that is the long-term goal unless the ACA is repealed.
If it is part of your medical records then yes, it is a possibility. All of that info transfers to a new Doctor. If you took the drug test for like a parole officer or treatment center that will not be part of your actual medical record and therefore will not be seen.
They will know if you are going to multiple doctors.
I'm not sure there's a database, but when your records are requested from previous dr it should be in there. What type of dr are you trying to go to?