I would revisit the situation in prayer if I were you.
In scripture it is talking about using the covering in their culture to show if they are married or not. In a society that does not use coverings for that purpose a wedding band or another symbol of marriage is fine.
My Bible study notes on that passage...
1 Cor. 11:56 head uncovered. A married woman who uncovered her head in public would have brought shame to her husband. The action may have connoted sexual availability or may simply have been a sign of being unmarried. In cultures where womens head coverings are not a sign of being married, wives do not need to cover their heads in worship, but they could obey this command by wearing some other physical symbol of being married (such as a wedding ring). While a shaven head or short hair was considered shameful for a woman in first-century Corinth, long hair was considered to be a womans glory
If the above were referring to just the spiritual/authoritative head, then why should a woman be shaved or shorn if not covered? What in the world would her hair have to do with it? Do you see the two heads? They are clearly the physical head, and the spiritual head, which stands for authority.
In verse 3, we see that the woman's husband is her spiritual head. What about unmarried women? When a woman is not married, if she is still living at home, then her father is her authority - he is the one taking care of her, and while she is under his roof, she is to submit to him. The single woman who is living on her own is not under the headship of her father, because he is no longer taking care of her - she is on her own. Therefore, until she marries, if she does, her spiritual head is Christ:
"There is difference also between a wife and a virgin. The unmarried woman careth for the things of the Lord, that she may be holy both in body and in spirit: but she that is married careth for the things of the world, how she may please her husband." -1 Corinthians 7:34
Let us move on. Verse four makes it clear that there are the two heads - the spiritual and physical, else one would have to seriously allegorize this verse, instead of taking it at face value. This verse also makes it clear that the headcovering is not hair, else all Christian men should be bald when they pray. For a man to take off his hair when he prays or prophesies is not what this verse is obviously talking about. 1 Corinthians 11:2-16 is referring to a physical headcovering that sits on top of the hair.
Now look at verses 5 and 6. In verse 5, notice that if a woman prophesies without a covering on her head, then she is dishonoring her spiritual head - her husband. This jives perfectly with other Scriptures, such as the following: