Mini Peppers are dying....help?

I'm new here so l'm hoping I came to the wrong place. I'm sorry if this is not. My 8 year-old son planted about 6 mini pepper seeds a few months ago in a small pot that's the size of a large coffee mug. They were growing well and seemed very healthy as they were bushy and strong. I knew I had to transplant them into their own pots as they were very close together in a confined area. Once I did, they seemed ok for a few days, but then started losing leaves. I live in Phoenix so we get a whole lot of sunshine and I kept them inside next to a window. This is what they look like now. I may have over-watered them when I transplanted them as well. I put then outside for a couple of days in hours that direct sunlight would help, but didn't seem to. Would this cause this? Are they a lost? Can I save them? My son is devastated as they were his little babies. TLDR: Mini Peppers are dying after transplant.