Now that my mother has passed away, do I have to share money with my brother if it was in the account that she and I had jointly?
In Texas, no, assuming it's actually a joint account or payable on death. However, it sounds like you might have been able to write checks and such for your mother, and that can be accomplished without actually creating a joint account.
Elderly folks who want to have a son or daughter with the power to write checks and such should consider accomplishing that goal by a power of attorney rather than by a joint account (or keep the joint account to a minimum). A joint account can create confusion during life (such as during your son or daughter's divorce) and can undermine your wishes after death (as in the case where a sibling wants to avoid sharing an inheritance).