Getting rear ended and sustaining a whiplash means your brain bounced back and forth numerous times. This can cause diffuse axonal injury and/or a coup-contrecoup injury where the brain bounces into both sides of the skull. Your neck whipped back and forth and so did

your head and thus your brain. My second concussion was the same as yours. Sitting at a light and got rear ended. I too did not realized I was concussed though I had a terrible whiplash; I thought I was upset and frazzled. Luckily a doctor told me I had a concussion

which explained why I had trouble finding my way to work! Unfortunately, like you, I sustained another within six weeks. Here a good link describing whiplash and concussions.
https://www.youtube.com/watch?v=6wCgmaG3Zgw. Hopefully I am able to post a link here!