If this is on an outside wall, you may have split copper piping to the tub spout due to freezing.
After my power was out for four days (ice storms in SWVA) I discovered that both my tub spouts were leaking water dramatically while the shower head sprayed at a lower capacity. I checked my sediment filter, replaced it, and tested to make sure I had full flow. What could it be?
Whatever it is, it should have NOTHING to do with the power outage. The spouts leaking and the poor shower flow are also probably caused by two different problems. Call a plumber to fix the valves. The pipe to the tub spout should not have had any water in it so it should not have frozen or broke.
Licensed residential and commercial plumber