Let me disclose immediately that a plumber is not required to fix a leaky shower head.
The common issue with a leaky shower head is a bad washer. Save yourself some money and fix your own shower head leak in less than 5 minutes and for as little as $1.
remove the shower head, sometimes using an adjustable wrench will help
check the condition of the rubber gasket inside the shower head. *Hint* - If this part leaves a black residue on your hands, it's time for replacement.
using the same size washer, push the new washer into place. The ring must be placed flat inside the shower head assembly
now wrap Teflon tape around the pipe threads in the same directions as the threads
put the shower head back on making sure it's fairly tight
It's now time to check for any leaks. If there are no leaks, then congratulations!
But if the leak persists, you may have to unscrew the shower head and screw it back.