Iphone 6 touch screen has broken

After update for this new IOS 10 my touch screen doesn’t work well anymore.

I don’t know what happened. I did NOT drop the phone, nothing fiscally occurred.

Some greys bar appeared and the screen turned striped or plaid, or completely white or diaphanous and the touch stop to work.

It has been about 20 days that the guaranty expired. And when I took to support they told me that as I did not have the guaranty, they chance my iphone for a new one, but in exchange for something like $450.

THIS IS NOT FAIR! I don’t know if is iphone disease. My I did not break my phone! It wasn’t my fault! And now a must pay for another one?

I need help! When I tried to book genius bar in my town, do not show schedule available. I don’t know what to do.