In a grim way, I'm lucky to be British at this time. I can order my meds via the NHS app so have a reminder to do so on the Monday before I get paid. That way they're usually available to be collected on pay day. There's no physical interaction with any medical professionals, save for collecting the pills from the pharmacy as and when I'm passing by.
In terms of appointments for aftercare, etc: I moved to an area covered by a different ADHD service two years ago, and have yet to be officially added to the registers of the service that covers where I now live. So I'm unlikely to miss an appointment because I literally have no one to make appointments with. If I need a review, I have to make an appointment with a Dr, who takes notes on what I need and passes them on to the service, who reply when they can to give the Dr permission to change what I'm on, or increase my dosage.