You are either having drainage, damper problems, or a defrost problem either one will restrict air flow to the fresh food compartment. Start by inspecting the freezer compartment does it have excessive frost build up behind back panel or possibly ice under the panel at the bottom of the freezer.
Send a model number with You reply and I will help You get started on this
Clear out the freezer if not already done, remove the ice maker if equiped.
remove bottom panel from freezer by pulling plastic plugs from front edge>
Then remove back panel, has a few 1/4 hex head screws then release ground wire and ice maker harness>
You are most likely going to see the tray below the coil frozen over, using warm water or a hair dryer get this thawled out, then poor a few cups of hot water down the drain in the drip tray below the coil until it drains on its own.
Let me know how it goes
I look forward to Your response.
Was the coil iced up?
or just the drain and vent where iced over?
If it was the coil You have a defrost problem and its not going to last very long then it will be pluged up with ice again Please respond so We can get the defrost problem fixed if need be.