For some reason, 从[person] is considered a grammar error in Chinese (this grammar point often arises as an exam question). My understanding is that after 从 we should add a place, not a person (despite being able to say e.g. "learned that from you" in English). So afterwards we add a 那儿 or 那里 or something similar:
I heard from a friend you passed the test.
I learned that word from my girlfriend.
(And 奴 [part of 奴隶 = "slave"] is a typo for 女.)
For the desired expression ("I've been learning (Chinese) from my Girlfriend"), I'd suggest something like:
Recently, my girlfriend has been helping me learn Chinese.
In regards to using 向……学习, the Chinese Grammar Wiki writes about this:
Whereas in English we would say "learn from someone," in Chinese this would be expressed as "learn toward someone," as in the following example (and famous propaganda slogan):
Learn from Comrade Lei Feng!
The relevant definition for 向 is "towards", and it's used as a preposition, but since we don't use "towards" like that in English grammar (although it's used literally, like in "Muslims pray towards the Kaaba"), it won't appear in English translations. Another example is:
I should apologize to you.
In this example, we couldn't use "towards" in English.
The Google Translate sentence
would probably be interpret as habitual, not just a once-off. You can likely infer from context that it's referring to the recent time period, and it's ongoing.