My newborn currently at 23 day old and we encountered somehow the same during week 2- 3 where baby dun want to sleep in cot (she sleep in same room with us - aircon on 25 to 26 degree) / very fidgety when put down. We had numerous sleepless nights, taking turns to carry her. she fall asleep very fast in our arm / chest too..
we tried various ways - sleep in living room with matteress (no aircon, just fan), etc, eventually figured out that she didn't like to sleep in aircon room...
so now we didn't on aircon and she sleep quite well in the cot, only waking up for feeds and less fidgety..
i think it's about eventually figuring out what the baby wants (it's hard I swear lol), and yes it will get better, jiayou!!