First make sure you try to backup the phone by one of the means below.
Because it is not behaving properly I would try iCloud backup first even if you need to pay for more iCloud storage for a month.
How to back up your iPhone, iPad, and iPod touch - Apple Support
Let's make sure you did the Forced Restart correctly first.
Force restart iPhone – Apple Support (UK)
Then try this using a computer
If your iPhone is stuck on the Apple logo - Apple Support
or watch this video
https://youtu.be/2CRilTPouRU?t=97
There is no guarantee you can save any data since your last backup if you need to use the Restore option.
Daily iCloud backups or weekly computer backups are always recommended for such failures.
If no better you should arrange a repair iPhone Repair - Official Apple Support
Or
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