To be able to connect your phone to a monitor, you need a cable adapter compatible with the devices. However, we can't suggest you the right monitor for you because it depends on the specifications you're looking for (screen size, refresh rate, etc...)
I think so best curved monitors under $200 should be those having excess of features. As we say quality should match the price.
I found the AOC C24G1A for $169,99 on Amazon.
It doesn't have "Eye Comfort Shield" but has the Low Blue Light technology as well as FreeSync Premium. It also has 2 HDMI 2.0 ports, so that you can connect your computer and mobile phone.