An automotive A/C system can only cool the air x number of degrees below ambient temperature. I'm sorry, but I don't remember the figure any longer. It's a physics thing.
So yes, it's entirely possible that you are getting as much cooling as is possible. Changing your refrigerant is neither needed or required. It may however be low. Whatever gauge you have will show a different value depending on the outdoor temperature.
Your car will have a recirculate position on the A/C controls. When set on recirculate, a far greater percentage of cabin air will be recirculated through the A/C evaporator in comparison to the intake of outside air. It's easier to cool already cooled air that air at outside temperature. This will allow for a lower output temp than during normal operation.
Only a shop will be able to tell you if you need more refrigerant by using a set of gauges.
Hope this helps.