There are several problems other than low freon. I expect that an appliance repair place would be more useful than HVAC firm.
Please check the warranty, many refrigeration units have a warranty on the sealed system. Which would include the freon, compressor, etc.
A good repair tech will do several tests before putting manifold gages on the system. He should check the temperatures, amperage, and air flow through the unit before checking freon pressures. He should also listen to the unit, as sound can help with the diagnosis. Many sealed systems like yours don't need freon, but need other things.