Can I restore my iPhone without having to use the iTunes app I don't have any computer that has iTunes on it

Yes you can if your device is connected to Wifi or cellular network, and if it has Find My iPhone turned on. See the second set of instructions in this support article (Erase with iCloud):

If you forgot the passcode for your iPhone, iPad, or iPod touch, or your device is disabled - Apple Support

Cheers,

GB

Go to your County library.

No.

I don't know about your library but here all they have is Windows PC without any iTunes on them.

Then he loses.