I'd have to say that this is some type of die-off. Maybe lyme but very well could be babesia. I do remember back years ago throughout my treatment that I did get dizzy or clumbsy tipsy drunk feeling from time to time throughout the day. And just like you, it wasn't everyday. And i had the strange sensations in the sinuses, and some pains behind the eyes. Gosh, thinking back, which of my 70 symptoms didn't get exaggerated due to herxing.
If you notice it more every 3rd or 4th day then this may be babesia you are affecting. Doxy and biaxin both affect babesia so it would all make sense. They are not the big babesia meds but they do have an minimal effect on it and if you do have babesia hiding within your body, it doesn't like it either.
Your extreme fatigue does sound more like a herx to me back when you first started doxy. I did a year of doxy before i found biaxin. And even after a year of doxy. The first week or two of biaxin, i was sooooooooooooooooooo tired. It was a herx though, that fatigue eventually wore off after a few months.
The only med that i can honestly say had a dizzy/drunk/clumbsy side effect was Minocycline. I just didn't feel right on it. I felt it just about everyday and it wasn't a full blown vertigo but a very mild annoying case of it.
As far as yeast are concerned. Acidophilus really has nothing to do with friendly bacteria numbers throughout your body(head/sinues). Acidophilus only replenshes the good bacteria into your stomach, intestines and colon. It can replenish in your throat also if you take chewable acidophilus.