The big thing with ADD is that it is a developmental disorder. That is, it's not something that "just happens" when you're 20 or so. Do you remember having a hard time focusing in elementary school? If you're in high school now did you have these difficulties last year? Two years ago? Have you always been described as a "day-dreamer?"

Sometimes gifted kids fly under the radar in elementary school, meaning that teachers miss it, but usually kids start noticing it themselves in these cases.

IMHO what you're describing sounds like it could be ADD. Actually, the proper diagnosis is "Attention-Deficit/Hyperactivity Disorder - Predominantly Inattentive Subtype," or ADHD-PI, even if you have zero impulse control issues.

I guess my end advice would be to get further assessed - preferably by a child and adolescent psychologist who has experience with ADHD-PI (if they have no idea what that is walk away from them).