I have a Rheem split unit heater / ac RGDG-075AUER. It appear to be from 1994 based upon the serial number CB5D302-F1994-1196. The unit does not provide proper cooling for my townhome. When the AC is turned on it will initially blow cool air, but eventually the air appears warmer as if only a fan / blower is running. Earlier today when the AC unit was running I outside and checked the unit out side, the fan was not on at all.
Is there anything that I can do by myself or should I just contact my local HVAC repairman?

Sounds like you may have a motor gone bad or a capacitor. If you are not mechanical inclined and have tools it might be better to call for help. If you feel you can handle the situation fix it. Your choice.