Hi Windy. My DD (now 16 months) was exactly like this. If I needed a break for 10 minutes for a shower or something my husband found bouncing her in his arms next to his warm chest would settle her (and make her fall asleep - but not well enough to be put down!).
I did feed her all the time for the first few weeks though. It worked out well in the end as it helped bring up my milk supply for the growth spurts (which felt like they were every other day for the first month!)
In terms of night time, we found using a cot sheet I had been keeping up my jumper helped (it smelt of me, and was warm) and also helped to ease her down eeeever so gently after she had been asleep for long enough for me to be able to pick up her arm and drop it without her waking. It did not always work, and I am sure for the first couple of weeks we co-slept when I didn't want to.
We chose to co-sleep again from about 10 weeks (when she was bigger, and we had a sidecar cot) as it was so much easier in the night for feeding, and by that age, she was a master at feeding laying down, so she would roll towards me, latch on, feed, finish and roll away again without me really waking.
It is a hard time, and it feels like it is forever, and you are doing everything wrong, making rods for your backs, but you are not. It will be better in no time, and you will be worrying about something else (there is always something...)
Congratulations on your little one, I hope the swaddling works for you.