Amoxicillin is an antibiotic and Prednisone is a steroid. If you have an enlarged lymph node, its possibly due to infection, from the strep throat. I would say it is nothing to worry about, this is probably why you are on the Antibiotics and Steroids to start with. Feel Better, and Good-Luck.
I would think that the lymph nodes would be swollen due to the infection. In fact that is one of the symptoms of an infection.
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They are giving you these meds because your lymph nodes are swollen and infected. Hope you feel better soon. Peace