I left my hotel and checked into another without informing my travel company, can I get a refund?

You are not automatically entitled to a refund for your extra costs. By not informing your travel company of your complaint and intention to change hotels, you did not give your travel company the opportunity to sort the matter out. Therefore, they cannot be expected to pay for something they weren’t aware of.

Remember
If you did not contact the company at the time of changing hotels, you did not mitigate (lessen) your loss.
As per their terms and conditions that you agreed to, you should have contacted them immediately with your complaint.