Fragment, as we don't know who the subject of the sentence is. Who is really sobbing?
How about this one? A little scared, I headed for El Building.
Would it be a fragment or simple sentence?
A simple sentence with an introductory adjective phrase.
Yes, you're correct. "Not just silent adult tears, but really sobbing" is a fragment. A simple sentence should have a subject and a verb that forms a complete thought. In this case, there is no subject or verb, so it doesn't form a complete thought. It seems to be missing information and does not express a complete idea or make sense on its own.