If the LED indacators show that the heat pump is running in cooling mode this is what it should be doing.
Cold air coming from the vents is a good indicator that it is working properly. It sounds like you have an air flow problem through your house. If your Carrier controller is not allowing the dampers to open in some rooms this will need repair. The controller is an important unit. Hard to say if the tech loosened a wire when working on the unit but somethimes this does happen. Did the tech provide a solution and price?