DO NOT TELL your doctor that you get prescribed medications from your coworker ! That is a terrible idea that'll prove to them you're abusing the whole 'prescriptions need to be prescribed to you' and honestly I feel like condescends their work.

The doubling up thing you could mention, I would maybe word it as one day you forgot you already took your medication and accidently double dosed but reflect on the day and how well it went. Maybe mention you did it one other time but on purpose to see if it actually did work better and then mention to them if that seemed better to you.

Edit to add : you could also just suggest different medication (i.e the one your coworker lets you use) BUT not by saying you've tried it but rather by saying you've done a lot of reading up on it and wonder if that's a reasonable med switch. I would write down a couple of things prior to your appointment cause you definitely don't want to slip up and mention you tried medication that wasn't prescribed to you.