How to put iPhone in recovery

First back it up. Putting it in recovery will wipe it.

How to back up your iPhone, iPad, and iPod touch - Apple Support

Then next thing I advise is to try a Forced restart 

Force restart iPhone – Apple Support (UK) 

If no better you could Backup, restore to factory, then restore from the backup:-  

If necessary set up without restoring backup and test at that point, erase again, then restore from the backup:-  

(If the phone needs attention you will have to do this anyway) 

See here for the resources you need. Allow a couple of hours: 

How to back up your iPhone, iPad, and iPod touch - Apple Support 

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

Restore your iPhone, iPad, or iPod touch from a backup - Apple Support

After that arrange a repair for possible hardware failure 

Click here > iPhone Repair & Service - Apple Support 

Or  

Click here >  Contact - Official Apple Support 

Anything other than Screen or Battery may be a replacement phone and the price is in the article under "Other damage" 

See also:  Get your iPhone, iPad, or iPod touch ready for service - Apple Support 

Perform a Forced Restart on the phone. Follow the instructions very carefully. Users often do not perform the 3rd step correctly. Hold the button down until the Apple logo appears on the screen. If a slide to power option appears, ignore that screen and continue holding the button down.

Force restart iPhone - Apple Support

Normally, there are only two results from the Forced Restart:

1) The phone's operation returns to normal...or...

2) There is a hardware issue on the phone that will require the attention of the Apple Store or authorized Apple Service shop

If you want to try Recovery, it will not hurt, but I doubt that it will help.