jlee-
I would think that all you would see would be the phrase "drug screen" written on the prescription. There is a small chance you could see a different word in front of screen. If you were suspected of using hydrocodone you would be suspected of using meth, benzos, cannabis, and everything else. What ever is written, it is going to have you checked for a whole bunch of stuff.
In my youth, I would always worry about getting pulled over because I was nearly always guilty of something. It is amazing how clean living reduces your anxiety when driving. Well, let me rephrase that. I am still anxious when driving because of all the lunatics on the road. But I have very little anxiety about being pulled over. I can blow, pee, or walk the line (aka- the field sobriety test) with the soberest of them.
I would strongly urge you to do what it takes to get yourself clean.
JayR