C.V.
Infants with yeast infections (called thrush) may avoid solids due to the sore throat it causes. Thrush can be diagnosed easily by a thick white coating on the tongue and throat. Sore throats in general may cause difficulty swallowing anything besides breast milk. Dont worry if you breast feed while you eat you are setting the right example. My son went from brest milk to scooping food right off my plate when he had watched me eat long enough.
He also would not take formula for the same reason you describe (illness followed by aversion.) Good Luck hope all is well.