Can you give someone Chlamydia if they wear protection?

I just recently found out I have Chlamydia, I contracted it from my ex boyfriend about a year ago, although just four months ago I had a pap test and the results came up as a false negative. I was having a lot of discharge and my doctor thought it was just Bacterial Vaginosis, so instead she gave me medication for BV, well within the last couple weeks I began having the same symptoms, but worse so I went to the doctors and it turns out I have chlamydia. I'm worried though about a week ago though I started sleeping with someone new, using protection, he wore a condom, but I'm worried that maybe I still may have given it to him. I never would've slept with him if I knew I was infected, and I'm really embarred. My doctor says I have to give up the names of who I have slept with, so they can contact the people and treat them in case I spread it to anyone.. This guy is new to town and I'm worried if the clinic makes a call to him that he'll be able to figure out that its me. I don't know if its worth worrying about he did wear protection.. help please?