I have an emergency and need to get somewhere quick. What are my options?

If it's really an emergency (life or death) then probably your best (quickest) option is going to travel on a commercial airline (possibly funded by your unit so check). However, if you must use unfunded Space-A travel then the local installation commander may upgrade your category priority (to no higher than the bottom of the CAT-I) for emergency or extreme humanitarian reasons when the facts provided (validated by a competent and formal authority such as American Red Cross notification, unit commander’s memo, doctor’s letter, or by some other similar means) fully support such an exception (authority may be delegated the to no lower than the Chief of the Passenger Service Center or its equivalent).  The Emergency upgrade period for initial departure should generally be limited to one week however, this upgrade is not applicable for return transportation.   Ref DoDI 4515.13, Section 4.1.F and AMCI24-101V14, 14.9

DoD Civilians may also be eligible for CAT-I Space-A Travel - sample letter available from http://www.spacea.net/regulations-forms-letters

Per DoDI 1327.06 (Leave and Liberty Policy and Procedures), Emergency Leave is intended for "Immediate Family" which is defined as "A Service member’s parents, persons who have stood in "Loco Parentis", siblings, children, and the spouse’s parents and siblings."   "Loco Parentis" is Latin for "in the place of a parent" and refers to the legal responsibility of a person to take on some of the functions and responsibilities of a parent (i.e. the person provided for your physical and financial well being as a child).  Grandparents don't qualify as "immediate family" unless they raised you instead of a parent.  It helps if the "Loco Parentis" individual is already documented in DEERS.