Touch Screen Require Analog Pins that Omega doesn't have
Are they any touch screens that aren't reliant on analog pins?
As I've come to realise that unlike the Arduino Uno the Omega2+ doesn't have an analog pins so I'm not exactly sure what to use
There are touch panels that is using I2C as interface to uP/processor.
They cost more and kind of uncommon.
One thing to think about: balancing your components budget is a good engineering practice.
BTW, there were discussions on make sense or not on using a SoC that does not have a GPU/frame buffer... Again, engineering practices.
For low-cost, simple resistive touchscreen,
Adafruit has this
as dedicated resistive/analog to I2C/SPI conversion/reader (STMPE610 chip)