Keep talking to us on here - lots of us have felt the same.
I have had PND twice and BF twice on AD's to no ill effect. I remember feeling just how you did with DS at about the same time - sobbing that I just couldnt feed him again and to get him away from me.
What worked for me was two things - when I was completely exhausted I used to take him to bed with me (making sure things are safe of course) and just feed him there. I could doze, watch tv and he would feed on and off and sleep.
Also getting out and about helped. I remember sobbing to a brand new friend I had just made (she is still my friend lol) that I just couldnt carry on any more. I hadnt left the house in weeks- she took me straight out to starbucks and it worked wonders. From then on I went every single morning - seriously. It got me out of the house for a few hours, starbucks has comfy chairs (get there early) and are very supportive of breastfeeding. I used to chat to the old couples who were there. It saved my sanity. I then got the courage to go out to groups - BF support, just general groups. I also explained the situation to some good friends and got them to come over and sit with me sometimes - just having company made all the difference.
I got better, we BF for over a year. The same thing happened with DD (think its hormonal for me) but I knew what to expect. I went straight on the anti D's at 3 days and got myself out and about.
I'm not saying any of this is easy - I cried in the most embarassing places...marks and spencers, the HV clinic, work but it did get better. I used to enjoy the feeds - they do stop being so close together. 3 weeks is a classic time for a growth spurt... they do stop. Driving in the car, walking in the pram, wearing a sling - they all help.
You will get through this. If you choose to stop BF then that is your choice of course - but I dont think the situation will miraculously improve if you use formula. I bet it will still be you doing the feeds, the depression wont just lift. You might then actually end up feeling guilty or upset if you didnt want to stop. The anti d's need time to work - for me it took about 2 weeks for any effect, then a big improvement by 6 weeks and by 12 weeks I was absolutely fine - if anything a little too jolly .
Be kind to yourself - take all the offers of rest you can - get someone to take him out in the car, for a walk etc. Perhaps express some milk if you can and then he can have that.
We are all here for you - cat me if you like. Your message sounds so similar to how I felt I could have written it word for word. You dont have to deal with this on your own. xxx