You can install an app called "Battery Life" to check the health of the battery itself and make sure that isn't the core of the issue.
After launching the app, swipe to the third info screen and look at the following information:
- Capacity: Make sure that the two numbers match or are very close. The first number is the amount of charge capacity the battery will actually hold versus the total capacity of the battery when new. The further apart these numbers are, the more "worn" the battery is and the shorter time it will hold a charge. The very first info screen expresses this to you with a circle graph, a percentage, and a color. It will blatantly tell you the wear level as Pefect, good, bad, etc.
- Cycles: A cycle is equivalent to "one tank of gas" worth of miles in a car. It doesn't matter how many times you topped off the tank, you're counting the number of full charge's WORTH of battery use. The higher the number, the more likely the battery is to be worn. I've had phones with 400 cycles that showed very, very little wear (5% or less) and phones with 300 cycles that show 20% wear (very bad).
If your battery is worn, the issue is NOT the iOS update. If the battery shows generally very good health, then there's likely something in the 9.3.1 update that is combining with a setting or something that is running the battery down too quickly.
Go the Settings -> Battery and check to see what processes are showing at the top of the list.