it sounds like what your seeing are the heating coils which are usually behind the fridge, not inside of it. so if you pull the fridge out, you can get a better look at whats going on.
from your description, i'd guess HC is right and dust accumulated/something happened and the heating coils didn't absorb enough heat and transferred it to melt a seam away in the freezer. now the freezer is leaking onto the heating coils creating the sizzling sounds you hear.
i'd say for water damage reasons alone you probbly should tell your landlord about it. pull it out from the wall first and look at it to see if what i said is what seems to be happening. i'm a little surprised you haven't already had a water buildup if it is
also, here's a nice link on how fridges work
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what if nigger meant kite