I have successfully turned the defrost switch in the refrigerator, it clicked and have waited 10minutes no sound is being heard in either the fridge or the freezer...what is my next step?

Just checked again and I can hear the freezer dripping/defrosting. I am assuming if all is well that the timer should kick back into cooling? Update, it did kick back on but I noticed that at the back of the freezer there is ice build up so I am assuming that the coil is frozen and we need to take the back off of the fan and defrost it with a hairdryer? What is the part that we need to fix? I did have this exact same problem no less than a year ago on this same fridge and I had a repair person come in to do the work.

Thanks!!!