I don't think you're having a hardware problem at all. I think Apple's "fall detection" just isn't close to being ready for prime time. I'm totally disgusted with the feature.
I've got a friend with Parkinsons. His hands shake. He regularly gets a false fall detection just from hand shake, but since he has the watch has actually fallen hard four times and when he fell the watch didn't detect any of them.
My Apple Watch has given me several dozen false alarms. Any time I clap my hands together hard over my head at a concert it goes off. About 10-20% of the time when I'm in the kitchen chopping through poultry, smashing garlic, or shaking a half gallon of OJ hard it gives me a false alarm. This is totally reproducable. But the two times I've fallen hard, both from tripping over something on the floor in the middle of the night, it doesn't detect a fall.
Apple won't admit it, but they need to acknowledge they must work on fall detection and get it to actually work. The false alarms are annoying, but the falls, including the one I had last night which resulted in my head hitting the bed frame hard that weren't detected means this feature is an abject failure.