Thats exactly what that formula does...
$E$3:$E$19 is the range that contains all of the Categories in the table above
E22 contains the specific category you want the total for
$F$3:$F$19 contains range with the amounts for each of your categories

Is that not what you wanted? My calcs give exactly what your =SUM(ref,ref,ref) gives

D
E
F
21
Total Expenditures
22
-$85.60
 Restaurant
-85.6
23
-$32.72
 Computer
-32.72
24
-$408.87
 MasterCard Payment
-408.87
25
-$1,524.31
 Car
-1524.31
26
-$20.00
 Coffee
-20
27
-$75.56
 Alcohol
-75.56
28
-$15.44
 Groceries
-15.44
29
-$544.63
 Education
-544.63