Why would you have hot water in your bathroom sink but not in the bathtub shower?

Shower valve is bad. Replace it.

Ans 2 - Shower valves often become plugged with debris. Many of them can simply be cleaned by carefully removing the control lever and and ball and then picking out the debris. Be careful to lay all parts in order if you dismantle it.

This may take about an hour, but is generally much simpler than replacing the unit, especially if behind a tiled wall.