how if I have the shapefile off all us counties added to my TOC and all the shapes of the states, could I go in and individually change the color of each county to display the data I have collected?
You are looking for Symbology and particularly Color Ramp
Perhaps a Unique color ramp
This is from Pro's help... an identical topic exists for arcmap.
Basics of symbology are located within the same area
The only problem I have then, It does this for every county in the U.S. or whatever I have selected by attribute, not the specific county I am clicking on.
If you chose unique values, they would all get a unique color. If you want a particular color for each one, then you would have to do it manually. So reading a bit of some of the tutorials would help.
How to symbolize maps for instance http://pro.arcgis.com/en/pro-app/get-started/symbolize-your-data.htm