I would try the CLR approach too. If you have a high level of calcium in the water, shower heads and faucet aerator/screens can get calcium deposits right where the water exits the shower head or tip of the faucet. Have this problem at home on our well and have to use CLR on all of them throughout the house every year or two.
Could also be sediment in the head which would need to be flushed out. The shutoff valve on the hose could be plugged up. Temporarily remove that and see what the flow is like out the head. I would also undo the head off the hose and see if the flow is okay. If not, you could have sediment plugging up the valves and if washerless cartridges, need to be replaced. If you do find sediment, it may be a good idea to use a sediment filter if you frequent the same CGs.