Baby overheated 😢

I had an appointment at the chiropractor today and had to take my 8 week old son with me. He was asleep in his car seat when we arrived so I left him in the seat and just set it on the floor of the changing room attached to the chiropractor’s office with the door open. I was maybe 4 steps from him, but had him turned away from me because of the lights in the room. Midway through my adjustment, he woke up and started fussing. I thought for sure he would fall back asleep so waited a minute to see. All of the sudden he started screaming like I’ve never heard before!! My chiropractor finished the adjustment she was doing as quickly as she could and I went in to soothe little man. When I saw him, he was redder than I knew a baby could even get and just dripping with sweat from head to toe. This was in literally five minutes or less. I was horrified and started crying out of total fear. I unbuckled him as fast as I could and pulled him out and cooled him down. First of course I feel like a horrible mom for letting that happen...so many lessons learned and I’m just broken from it. My heart still aches when I think of his poor little body being so hot and he couldn’t do anything. But second, I’ve read overhearing can cause SIDS. Should I stay awake and watch him while he sleeps tonight? This was about noon today so almost 8 hours ago. I’m so worried. He’s been fine the rest of the day, just so over tired. Has taken his bottle just fine too. Help?!