Kayla, I would be more worried about your relationship than the housework to be honest. I don't think it's a good sign that he's so angry when you ask him to help.
I've had this problem (housework) with my DH, who lived with his parents before moving in with me (yep, definitely should have seen what was coming!). He would do nothing to help unless 'nagged', or as we prefer to call it, 'asked'. Then he would do it, but I would have to ask every single time, about every single thing and it drove me mad. After a few years of, essentially, mis-communication on both our parts, we sat down and had a big chat about it. I told him that it felt like he didn't care about me when he knew how much it meant to me to have him help with the housework, and he told me that he hadn't realised how much it meant to me (underlining the fact that some men do need to have things spelt out to them), and that to be honest he just didn't see the mess. Lots more besides, but the upshot is that we compromised, I accepted that he just wasn't that bothered about the house being a mess and so I couldn't really expect him to keep it to the same standards as me, while he accepted that the state of the house was upsetting me and so he offered to take on the washing full time (and with no tumble dryer, it is pretty full time), which frees me up to take care of the stuff he doesn't see.
It's working really well, as he's also been offering to help more when he gets in from work. He'll just ask whether I need any help with tea or if there's anything else I need done - normally I'll be so happy he asked, I'll just ask him to make us both a cuppa, or remind him that the washing needs hanging out - well, old habits die hard!
Sorry if that sounds a bit smug (have just read it back), but I'm just trying to point out that if you communicate properly and do genuinely love each other, then a compromise should be possible.
Good luck!