My boyfriend gave me syphilis 'from his ex' do you think he cheated?

My boyfriend and I have been together for about 5 months. A couple weeks ago he developed a sore so we both got checked. We both were positive for syphilis and got treated. I know I was clean before we got together. He says he must've gotten it from his ex and swears up and down that he didn't cheat. I don't believe him. At the doctor's office and online it says that sores will develop within 90 days of becoming infected. What do you think? Is it possible to not get a sore until after the 90 days?