The right side of my phone's display is not working

The touch screen digitizer has gone bad and most likely has to be replaced.

This is the repair guide on how to replace the digitizer.

Nokia Lumia 530 Touch screen, LCD Display Replacement

You can either buy the digitizer only or digitizer + LCD.

If you do buy the digitizer only. Please note you need soldering skills to join the digitizer flex cable golden connection points to the LCD's digitizer connector point on the flex cable.

So it's probably better to buy the digitizer + LCD, while it costs $20 more it is a lot less hassle to install.

Where to get the part with Digitizer + LCD + Frame:

http://www.ebay.com/itm/New-Black-LCD-To...

Where to get digitizer only:

http://www.ebay.com/itm/New-Black-Replac...

While it is $15 cheaper, you'll need to clean the adhesive on the frame of the LCD you are using if you're changing digitizer only. Also you'll need to clean the LCD if you make any fingerprint marks or smudges / dust on it. So I think it is better you get Digitizer + LCD + Frame.

Edit: Also some new digitizers don't come with screen adhesive pre applied to them. You may need to use some 3m double sided tape to keep the digitizer stuck to the frame.