There are no clear answers, unfortunately. Babesia usually produces 'drenching' sweats, where you have to change bedclothes and sometimes even the sheets, but not always. I only get light sweats until I lower my bacterial loads (in other words, as I treat the other infections and get closer to healing them), and then my Babesia symptoms really kick in when I start treating Babesia. This is actually not all that unusual for these infections.
But, Lyme can produce light sweats as well, and sometimes those drenching sweats, but not usually consistently like Babesia can cause.
I would be more likely to believe that you are herxing from the recent addition of azith. Please either start or increase your detoxing, as that will likely bring things under control again without you needing to lower your dosages.
Herb only treatment for Lyme & Bart ended 12/11 - no active symptoms for 2 yrs -Herb only treatment for Babesia ended 12/12www.healingwell.com/community/default.aspx?f=30&m=2977364
Had Lyme, Bart, Babs, RMSF, Ehrlichia, Myco, Anaplasmosis, EBV
New Lyme case 8/2014 - Healed 1/31/15 - unknowingly had Asymptomatic Babs and Asymptomatic Bart, being treated now though (2/2016)