Have a look at silent reflux - the acid burns the throat but doesn't come all the way up.
DS has it. He spent the first 8 weeks sleeping upright on either me or DH. On from that we found he would settle much better on his tummy. By this point we had him on a combination of meds and milk which had made a difference - it was trial and error with gaviscon, ranitidine, omeprazole, LF milk and CMP free milk. He settle ok on CMP free milk and omeprazole. He is 6m now and we have noticed a massive improvement in him. He still sleeps on his tummy but for the first time yesterday he managed to fall asleep on his back
If it isn't silent reflux, then it could just be that he is taking that little bit longer to adjust to the outside world. Think about it, ALL he has known is being carried around and swayed inside you - 24 hour comforting. All of a sudden, he's in a big wide world, completely different to his cosy womb. Google Dr Harvey Karp, He saved my sanity.
Not only could I not put my DS down, I also couldn't stand still with him - he had to be rocked/swayed constantly.
DH and I did shifts with him in his early weeks. I would get up at 1am and be with him tip 6pm to allow DH to get some sleep and go to work, then when DH came on from work, he'd take over with the bouncing/rocking/swaying while I made a quick tea and then jumped in bed for a bit of kip myself and then start again the next day - it was bloody hard work but honestly, my memories now are not as bad as I thought they were at the time!
It's frustrating when you can't get anything done but really, it's not long in the grand scheme of things. I found it best not to put demands on myself. If I got something anything done in the day it was a bonus, if I didn't manage anything, well what did it matter.
It took me a long time to just accept that that was what DS needed at the time and i'd like to think that if DC2 ever comes along, i'll be a bit better at just accepting whatever they throw at me in the early days.
It all sounds a bit doom and gloom which I don't mean it to so i'll end by saying that at 6m now, DS is going through a pretty easy phase. The hardest thing is finding somewhere to go each day that doesn't cost the earth to do as a full day in the house is still pretty hard as he gets bored which leads to cranky which quickly escalates to screaming mess.
Oh, and agree with the carrier option - a sling is what i've found to be the most comfortable, especially as he has got heavier.
Good luck, and enjoy and embrace those newborn cuddles - those early days are over in the blink of an eye.