My phone has been misbehaving lately, could it have been jailbroken?

If your device was purchased new and you have not gone through the steps to jailbreak your device, then you can be assured it is not jailbroken. The issues sound like you may need a screen replacement. If you screen is cracked, that would be your problem. First try to remove any cases/screen protectors to see if that solves your issues. As the following Support article states, if those don't work, you may need to contact Apple Support using the link on the page.

https://support.apple.com/en-us/102567

Jailbroken? Only if you did it. You more than likely have failing hardware, maybe a failing digitizer. Have it inspected by Apple or an authorized service center.