It doesn't sound like the pregnancy was from someone on January 2. Conception would have been at least a couple of weeks later.
There are other possible dates that she slept with other ppl during jan but don't know the dates however the guy on the the jan 2 also has a vasectomy but there is a tiny tear in it he did a sorem count there was a 1 in billion chance so idk he is doing a DNA test so gotta wait for the results to see I guess
You said the only day you had sex with your boyfriend was January 2. Did you have sex with ANYONE around the week of the 20th? Or nobody at all in January except on January 2?