My iPhone 6 is malfunctioning?

My phone just stopped working. It doesn't notify me when I get messages, and it's not giving me suggestions on Safari, every time I try to delete a picture it just pulls me out of the photos app, and it's not letting me screenshot anything. This all started like three hours ago

I'm sorry to hear about your issues concerning the iPhone 6. Alas, you are not alone.
In this case I would recommend you doing a hard reboot. Note: This may wipe all data from your phone and put it back to factory default settings, so it is best that you have all your data backed up on the iCloud or another cloud system of your choosing.
To proceed in a hard reboot please hold down the sleep/wake button and home button simultaneously. Continue to hold it until the Apple logo appears.
If once your iPhone is rebooted and the problem is still occurring I would then point you in the direction of going into your Settings > General > Reset and first resetting all of your settings. If still the problem is occurring, go back to the Reset menu but this time select: Erase All Content and Settings. This will without a doubt put your iPhone back to to factory settings so a backup of all your data is highly advised.
If all fails then it is time to call Apple.
Happy Phone Fixing!

Hard Reset may solve your problem, but let me warn you it will wipe all your data so make a backup first. You may also try Leo Privacy Guard for your device it's the best app when it comes to security.