Hello and thank you for your question.
I am sorry to hear you have been so ill for so long. It sounds that you do have several things going on at the same time. Your symptoms might have started out as a plain upper respiratory infection but since then have progressed. It is likely that you have sinusitis (infection in the sinuses) which is causing you to have post-nasal drip which is irritating your throat, causing sore throat and enlarged tonsils as well as going into your lungs causing you to cough.
So the treatment needs to be with antibiotics as well as with some conservative things such as Mucinex (which will help dry you up), saline nasal rinses (to get rid of some of the mucus in your sinuses), and a steroid nasal spray. Antibiotics which you have already been on (Zpack and Amoxicillin) are not very useful for sinusitis and I would recommend a different antibiotic such as Clarithromycin or Levaquin. Since it will be your 3rd dose of antibiotics in a relatively short period of time, I would recommend that along with antibiotics you take a course of probiotics which will help improve the growth of "good" bacteria in your gut which is killed off by antibiotics and prevent you from getting a gut infection from a triple antibiotic therapy. I would recommend starting probiotics along with the new antibiotic and continue for about 1-2 weeks after you stop antibiotic.
I hope you find this information helpful. Please feel free to follow-up with any other questions you might have.
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Best wishes and good luck,