Hi pinkypanther,
I understand partially how you must be feeling, as my dp had to go back to his business after only a week's leave when dd was born. He is out of the house from 9.30am to 9.30pm six days a week. He comes home for lunch, but only for an hour or so, and after about 30 mins or so together dd goes for her nap after lunch.
We both live in a different country from our families so it's just us. I didn't even have a cs but it was sooo hard! I desperately wished I could click my fingers and be at my mum's so many times when dd was a little baby. I got really down and ended up with pnd, which lasted until dd was 8 months old or so.
As others have said, go to your mum's for a while or get her to come to you. IMO your dh should be doing something around the house. And you say you have to clear up after him? Well if he's really messy he needs to sort himself out, and if you have really high standards, you need to lower them for your own mental health. Don't worry about housework, cooking and so on if you can't manage it. Get a cleaner if you can.
I understand what some have said about your dp maybe not realising his life has changed completely yet, whereas you have no choice as you've been plunged right into it! It helped me to keep asking dp to do specific things, asking politely and without nagging or huffing. I found that part of the problem was that I would just get on with things as I knew in my head what needed done, and then I'd end up frazzled. All I needed to do was say "dp, could you take out the rubbish/unload the dishwasher/change dd's nappy please?" And so on.. Ok, so he should have asked what needed done, or just noticed himself, rather than going off outside to drink his coffee and have a fag, but I decided to stop being hormonal and resentful and just kept asking for what I needed.
No-one is going to do it for you!!!!
For example on Sundays I would just say "could you look after dd for a while and I'm going for a bath/a walk/a cuppa and cake in my room?" Rather than waiting for him to offer and getting resentful.
After a few months and a lot of rages from both of us about "never having time for myself" and quite a few fights where I blamed him for not doing enough and him complaining about me asking him to do too much in the house, and we finally broke the pain barrier and got used to being parents! He started to do more bits around the house unprompted and we both complained a lot less.
So anyway sorry to ramble, but you the summary is you have to spell out what you need to your dh. Sounds like he needs to do a bit of work at home every day, within reason, spend some nice time together as a family on weekends going for a walk and a coffee and cake or whatever, and also a few hours alone for each of you doing something nice every Sunday or whenever.
Keep asking for what you need and be kind to yourself, it's so hard having your first baby!