Hi sansthwaites,
Welcome to the Apple Support Communities! I'm sorry to hear you are having these issues with your MacBook Air and your new display. I'm sure we can help you figure out what may be going on.
Based on your described model, it does appear that the Early 2014 MacBook Air should be able to output a somewhat higher resolution to an external display, as noted here:
- Intel HD Graphics 5000
- Dual display and video mirroring: Simultaneously supports full native resolution on the built-in display and up to 2560 by 1600 pixels on an external display, both at millions of colors
MacBook Air (13-inch, Early 2014) - Technical Specifications
However, the max resolution possible may be limited by the connection type, and/or the specific adapter you are using. For example, this Mini-DisplayPort-to-HDMI adapter supports up to 4K (~3840 x 2160) resolution:
Belkin 4K Mini DisplayPort to HDMI Adapter - Apple
...while this Mini-DisplayPort-to-HDMI adapter only supports 1920 x 1200:
Amazon.com: AmazonBasics Mini DisplayPort (Thunderbolt) to HDMI Adapter: Computers & Accessories
So how you connect to an external display can definitely affect the maximum resolution possible. In this particular case, though, I suspect that the issue is actually the display itself, as the Samsung S32E590C display appears to list a max resolution of 1920 x 1080:
Support - Curved Monitors S32E590C | Samsung Monitors
Hopefully this was helpful.
Cheers