But your case does not sound typical, except maybe for the tip. The best solution: The wounds on the tail can be cleaned and disinfected by a vet in sterile conditions, and Baytril given orally for three weeks.
If there is an ascending infection, amputation is made between the tail vertebrae one inch or more above the infection. It takes skill and experience. Once I did my own amputation at 2 inches above the tip, but I couldn't find the facet cleft, and the tail got re-infected worse. I felt real bad about that. Some sites on the internet describe bending and snapping, which creates a clean break between the facets, but that method is very uncontrolled. In that case I tried it but it was terrible and I couldn't go through with it. I've heard some vets can do it. Either way, the vet sews the skin at the edges of the amp to cover the end of the tail. It helps prevent reinfection and helps a new tail growth start off evenly and straight.
You don't know yet whether there are deep internal tissue damages inside the thicker parts. An x-ray would show broken vertebrae.
I suggest washing the tail with soap and warm water, dry it, and apply antibiotic cream to the upper skin wounds and the tip. I like Bacitracin, and dislike Neosporin because it can cause inflammation. Watch these very closely for the next two weeks to make sure they don't get worse. If they do, it's a genuine emergency that needs a real herp vet, no matter how far you need to drive. Check out online pics of iguanas who lost their entire tails, it's tragic.
keep in mind that iguanas heal very slowly. Good luck :-)