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White noise is fucking magic for newborns. I'm not kidding. Sometimes my son would settle three seconds after turning it on, from a full-on wail.
There are free apps for your phone. I used one in the car and while traveling (we used to hook it up to the stereo system and play it that way even). We have a machine for his bedroom that we still use.
I highly recommend reading about 'the 5s' (Happiest Baby on the Block - but a quick google will get you the gist if you're short on time and sleep, as I imagine you are) - it convinced me to keep giving swaddling a try, as he seemed to 'fight it' and want his hands in his mouth, but sure enough, after two days, it became a powerful sleep cue for him. My husband also became an expert at the baby jostle while shushing loud in his ear.
I also suggest looking into babywearing. For newborns, stretchy wraps can be great. I've also loved the mei tei for my older kiddo when he wants to be held and I need to get things done - infantino has a cheap but nice one, and you can often find it even cheaper used.
Hang in there. The early days are rough. It gets better.
ETA: This is the app we used - he likes the 'red noise' which is close to the 'white noise' setting on his machine.
I've used this one with my son since he was an infant. Never had any issues with it.