Fender bender

I was in a minor accident last month. Someone slammed on their brakes in front of me and I slammed on mine but unfortunately bumped into them. We were going maybe 15 miles per hour. There was no damage to either vehicle. Everyone was fine. We decided to take information anyway just in case and each went on our way. I have comprehensive insurance with Aviva. So I get a letter in the mail yesterday from a solicitor stating the driver is claiming whiplash. I get a letter in the mail today with his passenger claiming whiplash as well. I haven't been in an accident in over 15 years. When I was in one in the US, they made a claim against your insurance and no lawyers are involved. This is scaring the crap out of me! Does my insurance cover this like in the States? Or am I being sued personally? Like going to court sued? They didn't even have the driver correct. The paperwork says my fiance was driving and he doesn't even drive! He's a cyclist. And they say Americans are "sue happy." Ugh..

My Husband was in a fender bender last year and his insurance company said any letter's from lawyers forward it off to them.
But there was something of TV about people stopping suddenly and suing for whiplash.
The advice I gave my Husband was let the insurance company haggle it out, that's what you pay them for.