Is there any way for me to check that my Thevenin equivalent is correct?
How can I check to see if my answer is correct though?


The other answer is correct, in that you can use a simulator to check your work.

However, if a simulator is not handy (e.g., as is most often the case on exams), you can analyze the original circuit and your Thevenin model with a load resistor, determine the voltage drop on (or current flow through) the load resistor for both circuits, and compare the results. 

If your Thevenin model is correct, you get the same load voltage (or load current) in both the analysis of the original circuit and the analysis of the Thevenin model circuit.