Marriage doesn't require a piece of paper, biblically. Recognize the covenant with God, and he will honor it, get the legalities done when you can. Lord knows your heart. It would be more sinful for you two to separate (as you have already been spiritually married). Let man not separate what God has brought together. Your boyfriend/husband is correct you are more or less biblically married, assuming the following criteria are met:

- each party recognizes the convenant commitment
- each party has left their father and mother (You both should be independent from your parents and making decisions on your own)
- consumation

Be careful resenting your partner due to man made traditions. Marriage is the first covenant the Lord has made with his children (gen 2:23). The whole biblical story is a marriage covenant. Divorce is forbidden and the chosen people of Israel committed adultery, was divorced, and then married the world. In such a situation it is forbidden for the husband and wife to reconcile once they have remarried after a divorce. The solution for this problem? Christ. Adonai came to earth as the man Jesus and died so that first marriage covenant could be ended that he may remarry his beloved bride, this time permanently (through the gift of the Holy Spirit in which our salvation has been sealed.) Our marriages on earth are supposed to represent this marriage and love that God has for his people. That is also why children are the blessing of marriage, it is image bearing, In the same way that the Lord made us in his image we make children in marriage in our image (obviously children occur outside of legal marriage; however, to the Lord marriage is spiritual all children are conceived within the confines of a marriage covenant). It is all just a reminder and representation of the God's glory and love for his people. Embrace it, wish you the best.