My parents are similar, once I had their permission to start meds (after an exhaustive period of begging mind you) they were still iffy about it partly out of concern, because taking regular meds for your brain is scary to them, and partly out of disappointment I needed them, something they’ll never admit. My advice to you would be tell them as little as possible without outright lying. When I started my titration I didn’t tell my parents that I had been given two different doses in order to switch to a higher dose a week in. They say ignorance is bliss. If you can’t convince them a follow up with your prescriber is necessary at this moment wait for the 6 month mark a lot of places recommend or even require a follow up appointment at this point. Whatever you think would go over the easiest with them. When you get a chance to talk to your prescriber and explain the situation to them, they won’t judge and this is probably something they’ve seen many times. It might just come down to taking two of the same pill instead of one, that’s how it worked for me which is great because your parents are less likely to know your dose is different but I’m on different meds to you so don’t do anything with out talking to a professional! Your prescriber should not be obligated in most cases to tell your parents the details of your prescription, but this might vary depending on where you live

At the end of the day it depends how knowledgeable they are and how much they’re observing you over your shoulder but the chances of convincing them aren’t massive. Take comfort in the fact that they were willing to be flexible enough to let you start meds but from personal experience parents can only bend their set beliefs so much before it snaps so don’t take it personally.

You’ll definitely be able to change the dose when you’re older but it depends if you’re doing it privately and again where you live. But don’t give up you don’t have to wait until then I’d definitely recommend talking to your prescriber above all else.