Aw hairband, the first few weeks are punishingly hard work. I was totally shell shocked. Stupidly I tried to keep up with my normal old life, cleaning, housework, cooking complicated meals etc... nearly finished me off. From about 3 weeks I think we lived on takeaways until ds was about 7 months old
I'd echo what everyone else says, don't battle through, do take every opportunity to rest yourself, even 20 mins with your eyes closed in a dark room can be enough to keep you going for another 6 hours. If you can manage it try and get outside for a few hours daylight as often as possible. Ds was a Sept baby so by the time I was over the shock, the days were getting shorter and I used to march him around the park in semi gloom, but the fresh air really helps.
I was a bit shy about joining baby groups, I'm not terribly good at meeting new people, but something with an activity, like music classes at your local library or something similar gives you a bit of focus, so you're not fumbling around with the small talk. You may think it's ridiculous taking such a tiny baby to a music class, and indeed ds slept through most of his, but I always felt it was more for me than him. Just talking to another adult human felt fantastic.
Finally, it really really really does get better. I can't say when, because everyone's different, every baby's different, but it really really does. Eventually you'll look back and laugh at how hard everything was, and how easily you take it all in your stride. Good luck