Corinth had lots of Temple prostitutes and they would shave their heads so people would know who they were. If you watch of old WWII film, when the Americans freed the French, they rounded up all the women that were having sex with the Germans so they could have things and shaved all of their heads. Since Corinth is the only letter that mentions anything about head coverings, I wouldn't make a doctrine of it. Although I do have family that came our of a oneness movement that uses head coverings and they still do. I remember growing up when we were part of the RCC and they used to use fails for their heads.
I know of a pastor that is part of the Calvary Chapel movement that requires women to wear vials on their heads. If you read it in chapter 11, you can get the idea that it could be talking about the women's head is her husband and that he should be covered, but it also says that Christ is the Head of a man. So is it talking about being covered by an authority or actually wearing a head cover. The cultural background of Corinth could be talking about wearing head covers and if it is again it's a cultural thing in Corinth. If it's referring to a women should have her head covered by being married, it's still the only book that talks about it.
Here's something of interest, the Jewish men cover their heads when in the Synagogues and on the streets, they also use prayer shawl when praying and they wear then on their heads. Is that symbolic of Christ covering a man's head? One thing is for sure, the Church in corinth had lots of problems. From divisions of who they were following, to prayer, spiritual gifts in the Church assembly, Paul said they were very immature, they had a brother that was married to his step mother or his dad's ex-wife, Paul had them excommunicate him, then had to tell them to bring him back because he made it right. Out of all the Churches they were the ones that needed the most instruction. So maybe other assemblies used head coverings for the women, but Paul had to instruct Corinth because of their immaturity. It's hard to tell with them, it's never been something that I thought was a problem so I've never really study it.
After all that I when to read it and verse 16, says it all, "If anyone is inclined to be contentious, we have no such practice, nor do the churches of God." If you want to wear a head covering go ahead, but if someones going to argue with you about it, there's no such practice in the churches of God.