Before you buy anything, try white vinegar. Seriously! Pour a cup of vinegar into a plastic bag, tie it around your showerhead with a rubber band, and let it soak overnight. This dissolves hard-water scale like a science fair volcano.
It won’t soften the water permanently, but it will clean your showerhead so the water flows better. It’s like giving your shower a little de-stress vacation. Plus, your bathroom will smell like a pickle. (Some people love that. Maybe you’re one of them?)
If you’re brave, you can also boil vinegar and dip your showerhead in it. Just don’t burn yourself. Safety first, soft water second.