What should I do given my parents' desire for me to marry, my lack of mental preparedness for marriage, and my need to stay and care for my severely disabled brother whom my elderly parents cannot care for on their own?

You have done well by taking care of your brother, and this is an act of kindness towards him and your parents. Marriage is the Sunnah of the prophets and a human inclination. You have several solutions:

1. Hiring someone to take care of your brother if you have the financial means, or finding a benefactor to cover their salary.

2. Getting married and having your brother live with you so you can continue his care.

3. Finding someone who accepts marriage on the condition that you remain with your parents to care for your brother, and your husband either comes to you or you go out with him for periods.

If these solutions are not feasible, then there is no blame upon you for delaying marriage, as long as you do not fear fitnah. However, if you do fear it, then marriage is more befitting to safeguard your religion, for the care of your brother is not an obligation upon you, but rather a voluntary act of kindness.