As regards the inflamed tonsils.
Tonsils are structures within the mouth. They provide defense against foreign bodies. A tonsil is not a disease.
Sometimes, they can become infected. This infection can be due to viruses or bacteria or other microorganisms (germs).
Tonsillitis does not always require antibiotics treatment. After evaluation, the doctor decides which treatment is best for the tonsillitis

You can also ask the nurse which vaccines she said you missed.

The vaccines indicated on the chart given at the government hospitals are those approved and included in the NPI schedule. They are free. If they have been properly given then your baby is most likely free of the ailments being immunised against. It might not mean it is the reason your baby has been sick. What has your baby been diagnosed with during the sick episodes?