Do you mean 6 days after your break week? If so you are still protected, even during your break week. If you literally just started taking the pill and this is your first pack then you are not. Check your packet to see what it recommends.
As for the burden of birth control….. pumping your body with hormones is also “uncomfortable”. We are adults who are making decisions for ourselves - you both want to have sex without risking a pregnancy, right? Then he can freaking help out with that by wearing a condom if he needs to, it’s not that crazy. Sorry idk why I’m triggered by that right now lol. Boo hoo I don’t wanna wear a condom okay well I don’t wanna take a pill every single day either do I