Chosen Solution
My initial thought is that your phone may be suffering from the Apple Throttling but you say that your iPhone is on iOS 9.3.3. Still, I would consider checking the health of the battery. Use a battery utility, such as coconutBattery (for Mac) or 3uTools (for Windows). It will tell you what the health of the battery is. Anything less than 70-80% of design capacity will require replacement. Otherwise,I am concerned about the fact that the phone was dropped over time, which could cause some logic board issues. But try testing the battery first.
