Yeah, you'll want to bite your tongue regarding your injuries. I'm happy you went to see a doc - car accidents can be tricky because injury can rear its ugly head a long time later.
Not quite a car accident but basically the same thing - in the early eighties I was working for the govt in Germany and fell off the back of an army truck onto a gravel parking lot - the ladder attachment tore out of the truck as I got to the top and fell backwards with my legs tangled in rungs.
I dusted myself off and went back into the office. The first person I met said "why is there blood coming out of your sleeve?" I was directly across the street from the health clinic, so I wandered over there dripping blood. They spent a couple of hours picking gravel out of various limbs and other body parts and patching me up before sending me home. I was really sore, but thought I was basically OK.
The building I worked in had a door with two padlocks - one about knee height. About three weeks after the accident, I bent over to unlock the padlock and couldn't straighten back out again. I had thought I was all healed up, most of the scrapes were healed and I had been feeling fine.
They sent me to physical therapy and I was mostly fine until I moved to the UK, made a wrong move and couldn't move again. Oddly enough, whilr the MRI machine was mostly invented in the UK, nobody there had one and there was a 6 month wait for any sort of imaging, so they put me on pain meds - which I hated.
A year or so later I went to Germany on vacation, quit taking pain meds and couldn't move again and ended up in a hospital (that actually had an MRI machine). Turns out I have a squished L4/5 and spent two months in physical therapy. They suggested surgery and the doc said "Surgery works great, I've had it done three times and I feel fine now"
TL-DR You can feel fine and have an issue a long time later.
