I have experienced this exact problem in the past. I found a solution.
Remove the shower head using an adjustable wrench. Remove the plastic filter. Place shower head face down in a shallow bowl large enough to allow for the head to rest face down on the bottom.
Carefully pour vinegar through the head allowing it to collect and submerge the fact of the head completely. The idea here is that the vinegar will loosen any calcium build up in the head and on the face of the head (similar to cleaning a coffee maker). Allow the head to sit in the vinegar and soak.
Soak the plastic filter as well. Carefully brush both the face of the head and the filter with a dish brush or old tooth brush to remove any debris or calcium. This should open up all the holes and allow for water to pass through as intended.
Reinstall the head - using teflon tape on the threads.
I did this and the head returned to normal functioning. It has been about two years and the problem returned. I am cleaning the head again today.
I hope it works for you too.
Age: 35 to 44
Project Type: New
Ownership: 6-10 years
Skill Level: Intermediate