Hugs, lovely, these first weeks can be difficult.
Sounds like he's got some pain. What's your supply like? When he is actively feeding, how long does it take, how's his behaviour? The wind can be quite painful and if there's a bit too much milk for what he can cope with, he'll be wanting to suck constantly to help move his guts along and pass the wind (gaining a bit more gas in the process).
The first 3 months is known as the fourth trimester as I'm sure you've heard - really you can't spoil a baby at this point and if its going to save your sanity and help you keep on keeping DD entertained, pop him in a carrier/sling/wrap and let him nap that way if he will. Props are not the end of the world, they're really not. Sleep training is best done before 6 months, granted, by that's plenty of time away and if he's screaming that much, there's something more at issue than props.
Try some different dummy styles. DS took to a dummy and was happy with that but he was fed by syringe and finger in special care and took a dummy at 4 days old.
Perhaps get checked for tongue/lip tie too - maybe he's not transferring milk and is hungry all the time?