My boyfriend wants a paternity test

We separated on and off a couple times during the fall because we both thought we wanted different things out of life. Come the beginning of December we say screw it and get back together despite thinking we're headed in two different directions because we love each other. During the time we separated I sort of dated a coworker for maybe a few weeks. The last time I ever saw him was December fifth and the last time we had sex was probably the 3rd. My significant other and I officially got back together around the 8th of December, though we didn't have sex right away. According to the last ultra sound I got I am now 9 weeks and two days. When i got the ultra sound I was 6 weeks 5 days. This would put conception sometime around December 22-25. Now my boyfriend wants a paternity test even though once we got back together I was seeing absolutely no one else and he knows that. He says he just has doubts and thinks it will help him fully accept what is happening. I am embarrassed to go do a paternity test I feel like it will be humilitating but there's no reason an ultrasound could be that off could it? I had an IUD but had it removed mid November. I had a very light and short period around Decmber 8-10th I'm not totally sure. I read that it could have been implantation bleeding but it could have also been light because of the IUD right? I know I sound crazy but I just need some opinions/reassurance. I read that the earlier the ultra sound the more accurate it is. So at 7 weeks it couldn't have been that off right?