From the description you give I suspect you have a defrost problem. Once you see the frost in the freezer it has already built up and is most likely blocking the air circulation to the refrigerator section.
There is something you can try to check the cause of this problem. In the rear of the refrigerator where the compressor is on the left side, facing the rear, is a defrost timer. See the image below for a picture of a similar timer. It will be mounted and you may only see the small round knob. With a straight edge screwdriver (or a quarter) you can turn the small round knob clockwise very slowly. At some point it should click and the refrigerator should shut off. You would now be in defrost.
You can listen to the freezer section for the sizzle and pop of a defrost heater being on. If you hear something the defrost element is most likely working.
If you heat nothing then it is likely the defrost heat is bad.
Next give the time 30-40 minutes to turn the compressor back on and start cooling. If it does this then likely the defrost timer is okay. If it never starts running after 40 minutes then you can manually turn the timer till it clicks and starts the refrigerator running. If you have to manually advance the timer then the timer is most likely the problem.
Any parts you need can be obtained from the following link:
I hope this information is helpful to you.