Had meningitis from bad sinus infection. Cured, but does it mean I'll always immediately get it again if I get another sinus infection?

Unusual. Very unusual for a sinus infection to transform into meningitis. Some may recommend a careful evaluation for a defect in the bony lining of the sinus cavities that can transmit the infection, especially if this recurs. If found, the defect is repaired surgically.
Not necessarily. No, not necessarily. However, when you have the first signs of a sinus infection, you should see your doctor to get on the right treatments.