To get by (in your example): to pass or complete a task with average or acceptable results, just meeting one's basic needsI can't speak French very well but I always manage to get by with a dictionary and a few gestures.
I suppose we must not use get through here, why?
To get through: similar to getting by, regarding the completion of a task, but different in that it indicates working through difficult circumstances, and it does not include an indication that the results are average or barely acceptable. In fact, we could say: Learning French is difficult, but with the right program you can get through it and achieve a great level of French fluency.
Also: Getting through (something) needs an object, while getting by is used without an object, like your example.
In fact: Getting by something (with an object) means to pass it up or avoid it by going around it.
These are the differences that come to mind. Others are welcome to add.
Student or Learner