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The clicking noise you are hearing is most likely from a bad blend door motor inside of the dash. The gears are known to strip on the blend door motor and will prevent the vehicle from changing it from hot to cold.
The blend door motors are only around $50. Labor usually depends on the blend door location. I can look it up really quick?
It looks like they only take about an hour to change out. When you get home and turn the key on. When the clicking starts to happen you can use your hand under the dash to determine which motor is making the noise.
There are a couple of these plastic motors that control the heating and cooling. you just need to identify which one went bad.
Most of the motors are the same. When the noise happens I would just listen and see if you can pinpoint the sound. If you can do that and update me exactly where the sound is I can give you more exact details.
Ok can you see the motor that is making the noise?
If you look under the glove box with a flash light can you see it?