Possibly STI/STD?

So, I had an accident where I could've gotten an STD from an unknown man. I highly doubt that it happened but I had to be rushed to the hospital because I broke my jaw, had a serious cuncussion and needed stitches. They gave me several medications that I never finished but it was for STIs, even though STIs are sexually transmitted, is it possible to get sick from not finishing these medications? I was supposed to finish them and then get my blood drawn, but never finished them and still got my blood drawn.