Aria
Is it wrong if I say "I've picked them out"? Must I say "I've had them picked out"?

Because of the use of "since" in the sentence it needs to be used with the auxiliary verb had and the past participle to make a grammatically correct construction. If you wanted to use "I picked them out", you would need to replace "since" with "when". Ex: I have had them picked out since high school. Ex: I picked them out when I was in high school.