Cause of noisy shower?

If when take the shower head stops the noise it is something to do with shower head it self. Try to get a multi function one normally helps to take the noise away

Could be multiple things

The cartridge it's self also had it where it's been the toilet valve a tap washer or even the main stop tap it's self

Airlock or no brackets/clips on pipe work

Possible blocked strainers. If running on a combi boiler, this could be due to a blocked heat exchanger.
Larger shower head will not cure the core problem.

Based on your description, it sounds like the increased noise is likely due to higher water pressure flowing through the showerhead. If reducing the temperature or pressure of the water reduces the noise, then it's likely that the showerhead is experiencing a high pressure drop, causing the water to flow through the small openings in the head at a high velocity, which creates noise.

Removing the showerhead decreases the pressure drop and stops the noise, which indicates that the issue is most likely with the showerhead itself. A larger showerhead may help to reduce the noise, as it would allow for a larger opening and a lower pressure drop, which should reduce the velocity of the water and, therefore, the noise.

Before purchasing a new showerhead, you could try cleaning the existing one to ensure that there is no debris or mineral buildup that is causing the noise. If the noise persists after cleaning, then upgrading to a larger showerhead may be a good solution. Additionally, you may want to consider having a plumber check the water pressure in your home to ensure that it is within a safe range for your plumbing and fixtures