My doctor recommended Rogaine for acute Telogen Effluvium (post-op Forehead Reduction/Surgical Hairline Advancement) advice?

It would be best to discuss your issues with your doctor.  If you trusted your doctor with your surgery, it would be best to trust your doctor with post operative care and follow up.

It is a common misconception that using Rogaine (minoxidil) and then stopping it worsens hair loss.  The effects of minoxidil do not persist once it is stopped, so any improvement you've enjoyed will regress but you will not lose more hair than you would have otherwise.  Put another way, someone who uses minoxidil for three years and then stops will look the same a year or so later as he/she would have had he/she never used the product, but will not look worse.
That said, minoxidil may help hasten recovery from telogen effluvium so there is no reason not to try it until your hair comes back, especially if your surgeon has suggested it. 

Many doctors recommend the use of minoxidil for Telogen Effluvium.  Sometimes it works and many times it does not work