From a non-native's standpoint: Which dictionary should I pay attention to when I find semantically contradictory definitions of a word?
Solution 1:
Whenever two dictionaries disagree about anything, I think you should consider both.
Words often have different connotations, depending on the experiences and perspective of the person reading / hearing the words.
When you see two dictionaries that disagree about the definition or connotation of a word, that is an indication to you that the word may have different connotations to different people.
At some point, you might intend to say one thing, and have the person receiving the message come away with something else altogether.
In the case of this particular phrase, "go through" or "get through" I think it can be used with varying degrees of negative connotation, but it is sometimes used in a positive or neutral connotation by the people I interact with daily as a native American English speaker in the northeast United States.
A neutral example would be, "I'm just going to go through the answers one more time before I turn in my test." Or, "Once you go through the tunnel, take the next left."