As I'm not sure whether you were only looking for the methodological answers provided earlier, this is a more detailed answer to the calculation problem you were trying to solve in the first place, providing an answer to the question posed in the title of your question. It is based on the A320 Airport and Maintenance Planning Manual, which provides approximate dimensions of the aircraft.
For the wings and wing-like surfaces, details are as follows:
- Wing top surface: $99.7 m^2$ (excluding wingtips devices)
- Wingtip devices (normal, non-sharklet A320, both sides): $1.8m^2$
- Horizontal tailplane top surface: $27 m^2$
- Vertical tailplane (both sides): $43 m^2$
Counting horizontal wing and tailplane surfaces twice (upper and lower), that yields a total of $298.2m^2$. This does not properly account for thickness (using the factor $1.07$ mentioned by Daniel yields $319.074 m^2$) and movables (high-lift devices, control surfaces, etc).
For the fuselage and nacelles, only top surfaces are listed. Modelling these as simple cylinders therefore seems the best way to go. Based on a fuselage diameter of $4.14 m$ and a length of $37.57m$, that yields a surface area of about $488m^2$. Of course, the fuselage is not strictly cylindrical, but I'm assuming here that is offset by the fact that I'm not explicitly including the front and rear surfaces (of a closed cylinder). Nacelle dimensions are not specified (probably as that somewhat depends on engine type), but based on drawings, I'm estimating a length of $5 m$ and a diameter of $2.5m$, resulting in a total surface (again: cylindrical approximation) of $78.5 m^2$ for the two engines. For the pylons, lets add another $5m^2$ per side.
In total, that adds up to $872 m^2$ (or $902.874 m^2$ with the 1.07 thickness approximation). That corresponds nicely with the $900m^2$ you found online - and also shows your own calculation wasn't too far off (some 3%).