Hi Saralee:
The shower head is not going to be the issue here...the SHOWER VALVE is the culprit..
Is there a name on the shower valve..? How many handles at the shower valve?
Seems most likely that will need to get into the valve and replace a defective washer or cartridge assembly.
Get back to me with more info..see what we can come up with...MARK
Also, note..may be worth a call to your real estate agent to see if they can get a plumber out to fix this......most will, especially just 48 hrs. post purchase!!