Wow, there is so much great information available on the internet, especially youtube videos. You can learn all kinds of music theory online. Do some searches, I'll bet you'll find just about everything you'd want to know. Plus of course I assume your local library has books on the subject. I would pursue those avenues first, then determine if private lessons might help you go further. But you can learn a tremendous amount about music theory from just reading or watching videos. It really is not very complicated, you'll likely learn it in no time. I will say, once you learn about chord structures and how to play them differently across the keyboard, it does open up whole new worlds! It will definitely help you to play by ear, as you'll quickly recognize how different chords sound and typical progressions or arrangements*.
So go for it, and good luck!
*Hint: Once you've learned basic music theory/chords, I've found that one thing that helps me quickly figure out a piece by ear is to follow and learn the bass line. This works in all genres of music, including classical. Once you know what the bass line is doing and the chord being played with the bass, the rest follows very easily. Doing this I can usually quickly figure out a piece by ear identically or so close that any differences are beyond perception. The only exception is in cases where the music is so complex or there is so much happening that it's impossible to distinguish individual notes, in which cases sheet music will help.