If by drug history, you mean admit to ever consuming an illegal drug, even once, then yes this can make you inadmissible or require additional things like the testing you mentioned. My husband required additional year of testing as he admitted to using cannabis at university years before. He ended up receiving his visa before doing all the testing, he only did one round of testing in addition to his medical. The testing protocol Casablanca had required 4 tests, one a quarter.
OP did the doctor ask you if you had ever used drugs? If so, did you answer truthfully?