Don't fill out a new application. Phone the NSW Companion Card Freecall: 1800 893 044, and discuss the decision.
You may be advised to send new information that more clearly shows you meet the Companion Card eligibility criteria.
If you are still refused a card, you can then request a formal review of the decision in writing to:
Locked Bag 4028
Ashfield NSW 1800
Any new information you provide, with the information obtained in your original application, will be considered in the review process.
You will be notified of the outcome of the review in writing.