Can't speak to ivermectin/doxy, no experience with that. But some general thoughts on chronic Lyme disease and treatment--
I had a 4 or 5 yr ordeal with Lyme in my late teens/early 20s. Might have picked it up through cracks in my knuckles exposed to blood from butchering deer (I believe they are a host also), as I don't recall a tick bite that I was aware of. But who knows. My hair was a little longer then and maybe I just didn't notice. =)
It is a nasty organism with potentially very serious physical/neurological consequences and not to be taken lightly. It's a very 'stealthy' type of invader and in my understanding it actually burrows in and lives inside the body's cells once it's established, so it's very difficult to impact directly through conventional medical methods (antibiotics etc) and even to test for. Before that stage it lives more openly in the bloodstream so is more easily dealt with. If you have a tick bite with a bull's-eye rash, DO NOT wait around, go see the doctor as that is a key indicator.
Alternative/natural medicine seems to have far, far better success overall, and that is ultimately the path for me that led to figuring out what was going on, and then to an actual cure (symptoms gone for 8 yrs or more at this point, all tests negative). It's still a long process of course (I think it was about a year for me?), but there is hope (also for West Nile virus... different topic tho). There are a few approaches to be taken I believe, depending on the practitioner and their area of training, but overall it seems they focus on bolstering your body's own immune system coupled with something more direct to act against the Lyme itself (in my case, very targeted courses of homeopathics).
Not going to go too deep into a side topic of alternative medicine. That's a whole other bag of worms, and controversial for some, and I understand that. Just know it's out there, it worked for me, and anecdotally it has worked for many, MANY other people with chronic Lyme disease as well. The practitioner I worked with is Dr. Cory Carter of Alt Med Services, in Rapid City SD. His clinic has a website with contact info but idk if we're allowed to post that sort of thing.