Using condoms as the only method of birth control?

Hi everyone! I'm pretty worried, because my boyfriend and I are planning on having sex in a few days, and I'm not on birth control (we're both 17). He already bought condoms (Trojan ENZ) and isn't planning on finishing inside of me, but I'm still nervous. I don't want to take plan B afterwards as I heard it can make you really sick, and I normally don't react well to even the simplest medications. I'll also be ovulating/fertile, as I just finished my period two days ago. Will we be okay? Or should I call it off? I want to be as responsible/safe as possible as there's no way I could handle having a child right now.