Cats tail possible breakage?

My cat went outside for a couple of days and when he came back I noticed (where the cox ix of a human would be) there is a bump,and now his tail does not wag,lift up or move only slightly with nerves at the tip,im thinking he has been clipped by a car and broke his tail.Im wanting to take him to vets but mum says it will heal in time,im just scared of infection spreading and the cost of amputation what would your advise be?