Do you struggle with discarding your doodles, sketches and drawings no matter how bad they are objectively?

Not anymore.  Save the best. 

yes because my work isn't private, there is always someone 'looking' and will exploit it out to my face.

No, I have no problem with that.

No, I go back after at least three weeks and throw out what I do not want to keep. 

I don't draw, but I keep the things that I write. They're a part of me; I still have the papers that I wrote in university. I kept all of them. Unfortunately, the things I wrote in grade school, Jr, High, and High School are gone. I certainly can't say that I didn't write some crap, but it's still Smugley.  It still has some value to ME - if no one else. Self-criticism is the hardest - and worst - criticism of all.

It's a history of YOU, is it not?    If your "history" doesn't become a fire hazard, I suggest keeping it. It's a record of YOU, for yourself and others to enjoy (or not).