Duuude you gotta remember that in their world, Omegas are often treated as trash and people often look down on them. Nanao will obviously still have those beliefs as he's lived with them his entire life and it has obviously hurt him, it'll take some time for him to truly believe in Keiji.
Also I think Nanao's job is to be an escort, not a prostitute. He just took it upon himself to have sex with alphas to ruin their pride and yeah, that doesn't justify him having sex with random people. The reason why he wouldn't want to quit his job is because that's his livelihood, and when does he have the time to worry about shame when that job is what's putting food on the table and a roof over his head? He said it himself that it's not easy to get jobs as an alpha due to the heavy discrimination in society.
This Omega sucks! I mean the Alpha has more than proven to really care. Who wants to have their significant other being a prostitute? Keiji isn't in the wrong at all. He genuinely cares. Nanao is acting like a spoiled brat. You turned him down and told him they wouldn't see ach other anymore. So why is he upset he didn't call over a week? And now Keiji says I love you and he still refuses him. What a jerk! (︶︿︶)＝凸