Well how about this.. Does every blower speed work? If so, its your blower motor resistor, but I'm not thinking thats the problem because usually if its that the blower motor will continually run, just you wont be able to change the speeds.
What I would be leaning more towards is that it could be is your A/C evaporator is freezing up . What you can try is instead of when you start to get cold, don't turn down the blower speed, instead turn up the temp. (make it hotter), because whats i think is happening is your running your blower to slow and the condensation is freezing on the evaporator and literally blocking the flow of air. If you turn up the temp, the fan will be able to blow the condensation off before it freezes but the air coming out wont be so cold that it freezes you.
Then most likely if that works your probably just a little bit low on refrigerant since you said that this is a new problem. So take it in and have some one charge it. Don't try and charge it yourself with those little cans.
If they weren’t meant to be eaten, then why are they made of meat?