But bible says a woman's head should be covered or else her hair should be shaved off.
Are you bald?
1 Corinthians 11:5-6 KJV
But every woman that prayeth or prophesieth with her head uncovered dishonoureth her head: for that is even all one as if she were shaven. [6] For if the woman be not covered, let her also be shorn: but if it be a shame for a woman to be shorn or shaven, let her be covered.
This was told by Paul due to cultural issues in Corinth at the time. If I remember correctly, harlots and the like were shaving and wearing styles to flaunt their promiscuity. Hence it was disgraceful of the church women to do the same with their hair when they were married and portraying something they weren't.
This was an issue in the realm of being part of Egypt yet some not being separate. From my understanding, it was Paul's attempt to advise them in a way that wouldn't create contention but remedy the situation. It is optional to wear a covering and a woman may do what she pleased with her hair but in the specific case of Corinth it was to stop a specific behavior.