Firstly: great to hear you and your boyfriend have been tested. Condoms are often highly over-rated in the efficacy of protecting people from diseases, so having both been sensible enough to do the tests is even better! Kudos to you both. It shows you care about one another.
Second: I echo the sentiments of those that have already spoken - while I'm not familiar with the mini-pill, I also endorse the standard (which varies depending on pill and your cycle) of waiting a month.
Third: I relied on condoms and contraceptive and when we decided to have a child, I was pregnant the first attempt without contraception. I didn't know I was so fertile and previous mishaps that resulted in my paranoia and getting the emergency contraceptive probably saved me some headaches and a much different life.
My attitude here (is surely my own, but I do encourage it) - a little paranoia and extra protection while your body is adjusting is definitely worth it. While kids are great, it's better to be sure the person you are with is the one you want as your child's father and early in a relationship is not the time you want to find out
Good luck with your relationship. And if you're concerned about the type of pill you're on, you can always switch to something else. Everyone has different reactions to the pill and so what you may read about terrible side effects of one particular variety may not hold true for some one else. This comment is in no way reflective of the mini-pill - I'm speaking generally. I'm unfamiliar with what you have been given.