Heartstringz, it sounds like you are having an incredibly tough time. How old is your little one now?
There is some great advice here however I feel I need to say that the swing won't work for every baby. Our first son screamed constantly for the first 10 weeks of his life - he hated any position but being held upright. The car, the pram, the bouncer, the swing, the bath, his cot ... everything was a nightmare. I took him to so many doctors and got so much conflicting advice, but the worst was "he'll grow out of it after a few weeks"... When you are struggling to get through each day the thought of the next few weeks is enough to send you in to utter despair. Finally, at 10 weeks he was diagnosed with silent reflux. Four days after starting medication he was a different baby - he slept... for longer than 20 minutes... and in his bed and not my arms!
I just want to say that after the first few weeks of dealing with a constantly screaming baby, I realised I would just have to put him down so I could shower, eat and go to the toilet. Yes, it was hard hearing him cry however I had a wonderful child and maternal health nurse who stated plainly to me that if he was fed, dry, warm, secure etc. then a few minutes of crying so mummy could tend to her needs would not scar him (or me) for life. Yes, sometimes the screaming escalated and he would be even harder to settle, but I realised as the weight was falling off me and I was lacking energy that I needed to stop and eat or I'd be no good to anyone. My son is now a healthy, robust 7 year old, who incidentally is still on medication for his reflux.
Has he definitely been ruled out has having any allergies or reflux? I haven't read all your previous posts so not sure if you've gotten second opinions but may be worth looking into - we went to 4 doctors in the first 10 weeks of our son's life before his reflux diagnosis. Also, I know friends who have had babies with lactose intolerance who have been similarly unsettled.
I really hope you get some respite soon. Maybe just buy a second hand swing from gumtree so at least if it doesn't work you haven't spent a fortune.
Good luck and hang in there, there is life beyond a screaming newborn!