Seems I have a few bubbles to burst here.

First off, it's exceedingly rare to find ANY laptop where you can upgrade the graphics. A few really high end gaming laptops might have a few LIMITED options, but for the bulk of laptops (Apple's being no exception), the graphics chip is hard soldered right to the main board. At a minimum then, to upgrade, you'd have to manually desolder a couple hundred tiny little solder joints, then resolder them with the new chip. And the new chip may not have the same pin configuration, and then there's potential issues with the chipset, software, it gets to be a real mess.

The reason the new monitor looks blurry is because you're both running a non-native resolution AND a non-native aspect ratio. You have a widescreen monitor with a 16:9 aspect ratio, but you're using a letterbox 4:3 aspect ratio resolution. That's what the OS is trying to tell you when it says "stretched". It means it's stretching the image to fit.

If for some reason the image isn't filling the entire screen on it's native 1920x1080 resolution, then you may want to check a few things. If you're using a VGA connection, make sure you run the auto-adjust for the image, since it may just not be centered properly. If you're using a DVI or HDMI connection, then you may have a defective monitor.

Now, if things are too small for you to see at 1920x1080, then find a lower resolution that doesn't have "stretched" next to it. You might want to try 1280x720 which is pretty close to what you are using now, but a widescreen resolution.

Your MacBook's video chip should be plenty powerful to handle well beyond 1920x1080 as well. If the video chip couldn't handle 1920x1080, it wouldn't be listed as an option. This is an issue with the monitor. Either the image isn't centered properly, or the thing's defective.