sex without a condom?

So today I just got nexplanon implanted and I asked my obgyn if it was safe to have sex without a condom once the nexplanon works properly. She told me that I should use a condom in case my boyfriend has chlamydia. I have been having oral sex with him for months now and even a few times the condom broke(I took plan b no worries lol) but if I haven't been showing any symptoms of any stds is it safe to say he is std free? I know I am because my gynecologist tested me but do we need to go through the whole process of getting him tested or will we be fine? We both lost our virginity to each other so I don't know how he would have gotten an std in the first place