Why does scratching the back of my throat with my tongue result in more itching and a cold days following?

Two things...: One, the need to scratch the back of your throat may be started by early, early viral infection(cold) setting in as a mildly itchy throat from inflammation in the tissue is one of the first signs of a cold. Otherwise, if you did not have a viral infection already, itching there too much can cause inflammation, allowing the tissue to be more easily infected by a virus, leading to a cold.

Itching: Rubbing your throat with your tongue does not cause a cold. Colds are caused by viruses. So you will have early (prodromal) symptoms before all the cold symptoms manifest themselves.