I was just prescribed Avelox as part of my Lyme regimen, somit does indeed kill the Lyme bacteria.
I've had some recent experience with rashes on my shins, they can be a symptom of infection with strongyloides, a threadworm. A couple of species can be lifelong companions. Also possible is filariasis, an even smaller worm. Some antbiotics kill a bacterial symbiot that they can't live without. If you do a google image search of strongyloides cyst, you'll find a picture of a shin rash, an extreme example, but one that I have seen on some people I know.
Greetings --
Welcome to MedHelp.
No one here is medically trained that I know of (I'm certainly not), but these are good questions you are asking.
I'm not familiar with Avelox, but looked it up online. It's an antibiotic and therefore would treat bacterial (not viral) infections, and Lyme is indeed a bacterial infection. Symptoms vary from person to person and over time in the same person, so whether you have/had Lyme only a doc could say, and the docs are in disarray on accurate diagnosis and treatment of Lyme.
In your situation, I'd certainly mention the now-gone symptoms to the doc if they come back, explain about the good effect you had from a course of Avelox, and see what the doc says. There are a bunch of low-lying infections that could be what you had/have, and only a doc can tell for sure. If things don't sort out for you, then you might consider looking into Lyme further, and on that point we here might be able to give you some pointers.
Best wishes --