No news is good news.

If you are held up by the Psych Eval you usually know before you leave the Doctor's office.

Sounds like you will be surprised by a pleasant call in the not too distant future offering you a date and offering to answer any questions you have. The Manager who makes these calls works at least 9 to 5 with the new hires and makes the calls on weekends and after hours. Mine came at 19:30 on a Saturday.

Delta does carefully perform the background check, but as long as you were completely candid with your airlineapps submission you have nothing to worry about.