It's not impossible to earn more than $2k or even $3k; however, you will have to work your way up to it.
It might be a good idea to pursue some private education courses. See if your employer will subsidise such courses. Also ask them about your RoA (Route of Advancement). This will give you a better understanding of how your pay scale will progress, with or without a degree.
See here and decide if you really want a degree:
The Truth About Degree Holders | MoneySmart.sg
You can also try some of these tactics:
Get Paid More: How to Negotiate a Higher Salary | MoneySmart.sg
Best of luck!