Why would a healed man need cough syrup, or any other man-made medicine???

Jesus took coughing upon Himself so we would not have to sit around coughing and could be healed and free from that infirmity.
If it's something that comes from nature that God put here, no problem as God provided all the nourishment we need naturally. At least this doesn't damage the body, but provides nourishment.
But, anything containing alcohol should not be put in to the Temple of the Holy Ghost (our body) as it is a known carcinogen (cancer causing agent) which is harmful to the body.
We should not knowingly and willingly put harmful substances in to our bodies... that is IF we obey scripture and present our body as a livinf sacrifice unto the Lord.
Glad this is all cleared up...