I see two separate issues in the excellent description of the "problem."

1. I am 18, a female and come from a non-musical family.

2. I had classical singing lessons for two years and found out a lot about singing. Different techniques, breathing, diction, interpretation, reading, etc.

The question that needs to be asked, suggested especially by the first item:

What kind(s) of music are you listening to and what kinds of music are you trying to sing?

If your brief exposure, and late interest in music is based on "music" currently popular with many of those of your age, you need to understand (personal opinion) that many, if not most, "current pop" singers don't "sing in tune" and the best to be said about the backup "chord structure" of the songs is that it's "bizarre or non-existent."

It's difficult to guess what your "2 years of classical" might have included; but my early exposure to friends doing serious university level studies of "classical music" suggests that it would have emphasized solo voice training - tonal quality, range, and "lots of scale practice."

Those who have more typical early exposure generally get to start out with "kid songs" that mostly do have simple scale/chord structure, and progress through simple "chorus" types of songs - on to "choral music" and/or elementary band/orchestra ensemble pieces.

Most of the music considered suitable for "young learners" has very simple and consistent scales and consistent progressions (movements) of chords. Practice at singing (or playing an instrument) with this kind of music is the basis for "hearing the note in relation to the chord," which may be one of the "tricks" you have not yet developed.

My suggestion would be that you pick a kind of music with well-defined four-part harmony to practice, preferably with others to sing the parts, or if you're able with piano or other "harmony backup." It will be helpful to sing the "harmony parts" some, in addition to just the "lead lines."

The "ultimate four part harmony" probably is "barbershop" although "protestant hymns" are generally fairly consistent. (I don't know much avout the other kinds.) "Camp songs" usually are very simple, but not too often "harmonized," and you need the "harmony."

Surprisingly, "old country" (before about 1950?) usually has simple structure and is adaptable to short vocal range. (The short range means you can move the key easily to fit almost any voice, so you can practice singing parts other than the "lead" without putting the others out of their range, not that you shouldn't explore all of your range.) You don't have to learn to yodel - until later?.

Some folk music is fine for developing a sense of the relationship between the tones you're singing and the chords and progressions that the melody is based on; but quite a lot of it is "modal" and should be saved for later after you're more comfortable singing in major/minor scales.

"Mary had a Little Lamb" in four part harmony can be a rich experience, and is perhaps a level - not necessarily the song - you need to start. The point is to learn to sing "the intervals" rather than rigidly "in a key."

John