Can doctors get their information wrong?

Yesterday I got the implanon put in my arm and the doctor told me that "it would be effective almost immediately" after he put it in. About 10 minutes ago me and my boyfriend decided to have unprotected sex. I'm kind of worried because online it says it can only be effective immediately after putting it in IF you were on your first day of your cycle (I was not on my period) and my doctor told me that was false. He said the only reason they say this is so that people come in knowing that they couldn't be pregnant. I don't know if my doctor is wrong but I'm only 16 and getting pregnant would be devastating. Should I have trusted my doctor?