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.
They are giving you these meds because your lymph nodes are swollen and infected. Hope you feel better soon. Peace