That's totally normal! My ex and I split, and I started dating first while sharing 50% custody still felt odd when she brought another guy around.
Ultimately, unless you bail on your kids, you're going to be their dad. Rmeember that don’t put them in the middle or make them part of your concerns. That only makes the dynamic with your boys awkward, and they won’t feel comfortable.
Be a great dad, focus on your boys, and you’ll be just fine.