Yes, you can build a shower tent yourself. For this, you should have some manual skills and possess the appropriate tools and know how to use them.
It is generally possible to build a shower tent yourself. However, the materials are usually as expensive or even more expensive than if you buy a ready-made shower tent.
It is also not easy to build a stable and free-standing shower tent that is also easy to erect and dismantle and easy to transport.
In many camping and outdoor forums you will find more useful ideas and tips if you want to build a shower tent yourself.
However, you should note that in many cases it is cheaper and more practical in terms of materials and time to buy a shower tent.