You were rear ended Car A was totaled Mine had no damage you didnt claim it on your insurance what will happen?

If you do not feel like it is worth your time and resources to drive your car into their assessment shop, then you are by no means obligated to make a claim on your insurance, even if the other person was severely injured. Why? Because in a rear end accident, it's car A's fault, and unless you backed up into him (your fault) or someone slid him into you (which wouldn't be your fault, but whoever hit him from behind) then it will remain that way. And the best news, if the driver of A was injured, his insurance will be paying the bill, NOT YOURS.

In other Words, don't worry about it.