Legal Question in International Law in Louisiana

My understanding of the law regarding prescription medications is that it is illegal to have a prescription from anywhere (US, Canada, wherever) if you do not have a prescription from a doctor or nurse practitioner. However, if you do have one, I believe it is okay to get it from out of the country, so long as all you bring into this country is what you were prescribed for you own use.

I base this more on personal observation during trips abroad than a review of the law. Many people in California and Texas (especially elderly people) go to Mexico to get their medications, because they are cheaper there. They all declared them at the border and had no troubles bringing in their own medications after declaring them. However, they all had valid prescriptions.