Your school counselor or nurse might be able to help with this. Unfortunately if you're under the age of majority, and your parents won't take you to the doc for an evaluation, there's not necessarily all that much you can do (to my knowledge - maybe there are other ideas out there?)

Another tack to try with your dad is to take an online quiz (the long one) about Adult ADHD (you're close enough to adult to count for this purpose) and print out the results for him to see. Maybe that might help convince him?

Typically testing requires a visit to a psychiatrist. Sometimes they'll do a computer-based test (this is ideal since it's more "objective"). Either way, that's going to show up as an insurance claim (or cost you a ton out of pocket) and most of the time your folks will receive some notice that a claim was made, so if you went under insurance, even without their knowledge, they'd probably find out. And probably be less than thrilled about it.

Imagine the scenario where you go in, get diagnosed, and then what? Do you think your dad would be more understanding, or upset about the way you did that? My guess is you're best off trying to convince your dad first. One challenge is that this is often genetic, so if your dad has similar symptoms, your complaints may sound like "normal" stuff to him, whether or not it's considered "normal" by anyone else.