Donnie,

The amount of deceleration needed to cause a concussion without hitting your head is quite high. You would have to be thrown hard against your seat belt. If this happens, you will not be very aware of the head issues because you will be struggling to take a breath. Your seat belt will have traumatized your rib cage including possibly breaking your collar bone, your ribs, or cracking the cartilage that connects your ribs. It is a very painful injury. This takes an impact like hitting a large stopped vehicle like a truck while doing 35 miles per hour or more.

Such an injury will take a few weeks or more to recover from.

Getting rear ended will mean your head impacts the head rest. No car outside a drag race course will be able to accelerate fast enough to cause a sub-concussive impact. Even then you would need to hit your head against a solid object.

As was said, you may have strained your neck at the most. Rubber tires on dry pavement have a maximum ability to avoid skidding of about 1.5 G's. Add some whipping forces against the seat belt and you might reach 5 G's if the force was very quick. I doubt you even came close to 5 G's. Maybe 3 G's at the most. Not even enough to be considered a sub-concussive impact.

To suffer a concussion from a non-impact, you would need to be shaken violently for a extended period like riding over a bunch of speed bumps in quick succession. I can't imagine where you could find something like that.

So, you can let go of your anxieties about quick braking causing a head injury. Neck strain maybe but not likely.