Relationship advice.

When we found out I was pregnant (unexpectedly) I found a text conversation that he'd deleted between him and a female coworker. He says he was just overwhelmed and needed to talk to someone about the baby and everything. But I have no way of knowing that that's what it was about because it was deleted, and even so, I'm not okay with him talking to other girls about our shit and hiding it from me. (He and this girl weren't even close, if he had a female best friend it would've been different). But anyway, fast forward 5 months, in that time they have an annoying relationship that I just don't trust, like he always works way later when he's closing alone with her. Her and her fiancé broke up and she decides that she and my partner are now good friends and has long deep conversations about her feelings to my partner when I'm sitting at home depressed and he doesn't care about my feelings! This Friday night just gone he comes home from work (while id spent the whole night throwing up, sick as a dog) and I opened his phone to put an alarm on for the next morning, and I see a conversation between him and this girl, blatantly flirting, with winky faces and innuendo!!! I was soo cranky and haven't really spoken to him since. I love him and I don't want to keep fighting. I'm so upset and embarrassed. He's apologised and says he didn't mean anything by it and that he's not interested in her. If I wasn't about to have his baby I'd leave, or at least insist on a break. But I'm not working at the moment so there's no way I could support our child on my own. My question is, would I be completely out of line to ask him to find another job? He's just a delivery man and bartender at the moment so he wouldn't be giving up a good job or anything. I just refuse to sit at home and be made a fool out of while caring for his child while he's out doing whatever he wants, flirting with whoever he wants. I'm just so frustrated and confused :( please give me advice :(