Air-conditioning not blowing cold air

Is there any audible switching under the dashboard? Does the fan turn on or not?

 

More than likely enough freon has escaped form your system causing the low pressure valve to stop the compressor from activating. This is a safety mechanism to prevent damaging the AC compressor. You'll need it taken to an automotive HVAC shop for confirmation and system recharge. There could also be a puncture in your system from road debris, again, it needs to be checked out.

 

The good news is your car should have the low cost r134a refrigerant that can be bought anywhere.

The bad news is a refrigerant loss means a leak that should be repaired to avoid the same thing again. However there are some small leaks where a recharge might last a year.

There are less common issues like duct dampers in the dash failing but they are rare.

 

I do not know specifics about a Prius C, but a Gen 2 with a bad inverter cooling water pump will cause intermittent AC operation. If the inverter coolant becomes too warm due to the pump not functioning correctly, the inverter will deactivate the AC compressor power portion to minimize heat build up, yet give no codes. Sometimes people spend big $$ chasing an AC problem that is actually just a $130 coolant pump problem. Again, I don't know if the C is similar.

 

It is possible that there is a refrigerant leak in the air conditioning system. Is there any indication on the dashboard about errors?
You can’t fix this yourself; you’ll have to go to a repair shop.