Phone compromised?

There are a few things to check in this case:

Recognize and avoid phishing messages, phony support calls, and other scams - Apple Support

If you think your Apple ID has been compromised - Apple Support

Did you already have a look at the list of apps that use most of your battery life in Settings/Battery?

Force restarting your iPhone may help to clear minor software conflicts, that may result in more battery usage:

Force restart iPhone - Apple Support

You can also set your iPhone back to factory settings on your computer and set it up manually, without using the latest backup after that.

Restore your iPhone, iPad, or iPod to factory settings - Apple Support

If you feel an unauthorized person is remotely controlling or monitoring your device, then that is possible only if you have done one or more of the following Don'ts...

1. Don't hand over an iPhone to kids or to a stranger without Enabling Guided Access
2. Don't share Apple IDs
3. Don't Jailbreak
4. Don't share sensitive information pertaining to your device
5. Don't give in to Phishing
6. Don't plug in your device in Airports and Public places through third-party cables and trust the device. Beware of Juice Jacking. (Especially in India)
7. Don't leave your iPhone unlocked and unattended in public places like offices, schools, malls, etc.

If one of the above is true then quickly change the Apple ID Password and Return iPhone settings to their defaults.