The subject is much deeper than what is taught. The idea is that we must have power over our heads, which is Christ, for protection against evil. Do not overlook verse I Cor 11:10 where the woman must be covered to protect her from the ANGELS. This refers to Gen 6:1-4 when the sons of God, (fallen angels of Jude 6), came unto the daughters of men and took them as wives thus producing mixed children. This is what caused Noah's flood. In verse Gen 6:4 it mentions "ALSO AFTER THAT" meaning it will happen again in the future. This is why the woman must keep her head covered BECAUSE OF THE ANGELS that will come again in the end days, (Math 24:37-38). They are going to come looking for women to marry as before in the days of Noah.
Now understand that for a man to be covered with long hair at the time of their coming would be a shame, as it would mean they are looking to mix with the fallen angels which would be perverted. So the answer to your question is that it is okay to have long hair but understand what the scripture is referring to. Remember Jesus also had long hair and the head of Christ is God. Hope this helped. You and your girlfriend go in peace and keep the Lord as your head.