The following resources can be looked at for study on this topic as you seek to wrestle through multiple views.
Benjamin Merkle deals with this question, “Isn’t it inconsistent to reject Paul’s appeal for women to wear head coverings while affirming his command for women not to teach or have authority over men, since in both contexts Paul uses virtually the same (creation-related) reasoning?” Read here, this article is very helpful.
Little Bible Chapel Position paper, where Alexander Strauch is/was a pastor. They hold a view of wearing a type of shawl.
Ryan Fullerton’s two sermons, he holds the view the covering is the hair. Sermon 1 | Sermon 2
Reformed Books Online has different resources here.
John Piper has an APJ here: Is It Wrong for Men to Have Long Hair? and an article here: Creation, Culture, and Corinthian Prophetesses
BibleArc has a video paraphrasing this passage here Head Coverings: Cultural or Absolute? To view Andy Hubert’s paraphrase, go here.