You did a good thing. And you're certainly no idiot. By all means start the Doxy.
Just a couple of questions. Did you show the ARNP the picture of the rash? Did you ask how many cases of Lyme he has diagnosed and treated? Most of us hate to do that.
There is a lot of theory-crafting with Lyme - ie - "i read some guidelines so I'm an expert". Probably this was someone who hasn't treated a single case of LD.
Stay positive. We'll all be blown off for all kinds of reasons. It's no fun. But you should be your own advocate. That's 10 days of Doxy? That will give you some time, and could possibly do the job, tho it's not ideal.
I think a good next step would be to call Dr's offices. Say you have a picture of your bullseye rash and you're looking for a Dr. who has actually diagosed and treated LD. At least you can weed out all the "experts" who have read guidelines but never followed a case of LD.
There are links to sites where people can tell you which Drs in your area are Lyme Literate. Maybe someone else can post the links.
Hang in there. You're doing the right things.
Lyme, anxitey, depression, chronic C. Pnuemoniae
"... expect the unexpected ..." (O. Wilde)
"I am an old man and have known a great many troubles, but most of them never happened." (Mark Twain)