My original shower head holder is still working fine, and the industrial double sided tape is showing no sign of failure. But when I look at a design almost every day, I come up with improvements. 

There are now three positions for the shower head, and the model has been rejigged to need no support. The model does not require holes drilled into tiles.

Attach it to the wall with industrial double sided tape. The stuff from the supermarket will not stand the load and water. Clean the tiles thoroughly, with soap and water and then IPA, you want the tape to stick to the wall, not a layer of soap scum.

Print with the bottom of the bracket on the build plate, that way it needs no support and the layers will not tend to separate.

I used PETG, but any filament will probably work OK.