Is my husband cheating on me??

Mine and my husbands relationship hasn't been the best the past couple of months. We are struggling financially due to me taking a different job with a better work schedule but it also came with a $4 pay cut. So with me not bringing in as much as I was before things have been really tight here lately. He complains that he's unhappy because he is having to pay for my part of the car insurance and the phone bill. I am only 19 with a ticket and a couple wrecks on my insurance but it's only $130 a month just for me. I personally thought that when you got married everything was conjoined. Not husband paying his half and wife paying her half of things. But that's how he sees it. Anyways we've been arguing a lot the past couple of days and he finally tells me how he really feels. He pretty much said that I've supposedly tested him awful and all kind of mess. Which I will admit I have my flaws. But what woman doesn't? Well needless to say he told me that if I was to leave that I was not coming back. Making me feel like he wanted me to leave and not come back. He told me he wanted us to work on things but the ways he's acting it doesn't seem like he does. I'm not real sure why but he showed me the Facebook messages of him and this woman he used to have a fling with. I guess they messed around a time or two when they were both younger. Well a couple months ago she randomly adds him on Facebook and they've talked a time or two. Well she shows me messages tonight of where they talked yesterday. She told my husband that it was too bad that he was married these days and he replied with its good to know he has options and a winky face. What do I do about this? I understand him being unhappy with our financial situation but to go as far as messing with another woman while he's married and then showing me the messages? Is this a sign he's trying to push me away or get to leave or what? I really need advice on what I should do. I love my husband and want to work things out but it seems like he already has his mind set on what he wants.