I'm only new to the world of smartphones myself (is an S3 considered smart?) and I have an S6. (I miss my old Philips dumbfone.
)
The sorts of things I'd be focusing on are looking at the data usage, to see what has been using the most, and also the RAM.
Look for recent spikes in usage.
What new apps have been installed recently.
Is the phone (OS and apps) up to date.
Are you running any form of antivirus or other security on it.
All these and more can be found under the various sub-groups under settings.
Last but not least, it's starting to get old. I would guess it's possible the battery is simply on its way out.