2 year old child having fever cough cold

Hi My son (22 months) had fever (100) , cold ,cough on 4th Sep,21. Consulted online and got antibiotics 5 day course. Used it for 4 days, but fever used to come after 6 hrs everyday. So, took to pedatrician and he suggested for admission in hospital as fever is coming back. Blood report showed crp -8. I was told he is having phlegm in chest and that has to come out. Admitted in hospital for 5 days. Given pipzo inj 4/day and IV fluids. After doing blood test and confirming no infection, we got discharged on 13thsep. Given cough, cold syrup for home during discharge. He is normal and active for 1 day. He got fever , cold , cough again. Got blood test done again, Neutrophils 85, platelet 5L. Doc told infection came back , need to admit for one more week and increase dose of antibiot this time and send to culture also.For Now, He gave antibiot to use for 10 days, if no better result in 48hrs, need to admit. (cefpodoxime proxetil, Azithromycin, cold n cough med). Any suggestions for this?