I guess if Dr. H has that combo suggested, then it's definitely fine, but I would think you have your bases covered with the Azith and Plaquenil, based on each drug's function as covered here
www.treatlyme.net/treat-lyme-book/kills-lyme-germs-a-brief-antibiotic-guideThe doxy doesn't appear to do anything that the other two aren't already doing. But I'm not a scientist. :P