Hi Mjw11 and welcome to the forum!
"Diarrhea, nausea, and vomiting have been reported during treatment with minoxidil topical." http://www.drugs.com/sfx/minoxidil-t...e-effects.html
"Any other skin problems, an irritation, or a sunburn on the scalp—These conditions may cause too much topical minoxidil to be absorbed into the body and may increase the chance of side effects." http://www.mayoclinic.com/health/dru...N=before-using
So far this is all I could find concerning how long Minoxidil stays in the bloodstream: "Minoxidil has a blood half-life of about 4 hours, but I can not determine how long it hangs around the kidney, heart, or other organs when it is out of the blood." http://www.baldingblog.com/2006/04/2...ay-in-my-body/
There's much more reading in that link but I believe it will take more than 4 hours to be completely out of your system.
As a side note just so you know both Prednisone
have been linked to hair loss.
If you haven't already you should followup with your GI.