Hello~I am sorry you are having these issues.
It sounds to me like the infection has not been entirely killed, I highly suggest that you tell your PCP what is going on and ask if you need another course of antibiotics. Azithromycin is a very strong antibiotic, you may not need one that strong, but I think you definitely need something.
In the meantime, I would take a supplement called "Propolis' This is a product made by the bees, it is natures penicillin and kills off lots of infections, it can be purchased at any health food store. Also, add the herb echinacea, this is a another immune builder, along with Vitamins A, D and C.
As to removing your tonsils, that would be entirely up to your doctor, I am not sure if they do that as much these days.
I hope you start to feel better soon. God bless you.
You likely have Chlamydia Trachomatis Tonsillopharyngitis, which hasn't been resolved yet.
The issue may be with Azithromycin, which may have more bacteriostatic activity and less bactericidal activity against the Chlamydia Trachomatis bacterium (the probable infectious pathogen).
If the immune system is compromised, the Azithromycin's bacteriostatic action would be rather ineffective, since the immune system is less able to identify and destroy the now static bacteria.
Check with your treating doctor if Roxithromycin, might be a better option for you. It is from the same class of antibiotics ( macrolide antibiotic) as Azithromycin, and could possibly target Chlamydia Trachomatis better with more bacteriocidal activity.
When taking antibiotics, it is advisable to also take some quality probiotics, in order to replenish your healthy gut flora, which gets damaged by the antibiotics.
Getting some supplements to boost your immune system as SassyLassie suggested is a very good idea as well.