Is it possible to pair my iPhone with my car radio and my hearing aids at the same time.

I have never been able to make 2 bluetooth devices work at the same time with the phone

If it is paired with my car then it kicks off the bluetooth headphones and vice versa

Not sure there is a way to enable both

Don't know if this will work but it might be worth a try. You could connect the iPhone to the car radio using the USB charging cable. Some cars allow you to hear your phone when connected that way. Then try using BT for your hearing aids. Little to lose in trying.