Can you find a single example of a preacher being involved in a marriage in the Bible? Have a think about it. A preacher is never involved anywhere. In the detailed laws God gave the Israelites through Moses, did he ever say a priest had to perform a wedding for the marriage to be valid? In the New Testament, do we have any such command for Christian ministers?
There is not a single command or example of a preacher conducting a wedding anywhere in the scriptures.
Rather, we have the simple instruction:
Genesis 2:24 said:
Therefore shall a man leave his father and his mother, and shall cleave unto his wife: and they shall be one flesh.
Biblically, marriage is when you leave home, shack up together and have sex. Which you've done. So you're married. Even the promises you made to each other, although good, were not necessary for marriage. Marriage is an extremely simple matter.
Throughout history, "marriage" was simply the name for the relationship formed when a man and a woman started living together. Often this was celebrated with a religious ceremony, but that was not necessary. It was not until 1583, at the Council of Trent, that the Catholic church decreed that a marriage had to be performed by a priest for it to be valid. This was an extrabiblical instruction added because of the reformation, intended to reduce the number of Christians leaving the church and joining the Protestant churches by saying that they'd be living in sin if they didn't stay in the Catholic system. The Protestant reformers at the time insisted that marriage was not a religious matter, but a civil matter, so if it was to be regulated it would be a matter for the civil government - which started government marriage registration. Over time, both government marriage registration and a church ceremony have come to be seen as necessary for a marriage to be valid. But this is only a very recent blip in history. It is the result of questionable recent religious and political decisions. And it is not founded in the Bible at all.
Don't question the validity of your marriage. You're married, without a doubt.
I'll add a few illustrations to help you see this from a few different perspectives, hopefully to reassure you.
1) Homosexual marriage is becoming legal in different places around the world - it's just been legalised in our country for instance. A number of churches support it. So there are an increasing number of homosexual couples who have been married both by a preacher and in the eyes of the law. Are these real marriages? If marriage is something that is signed off by a preacher, then they're married and you're not. If marriage is as defined in Genesis 2:24, then you're married and they're not. Which sounds correct?
2) If marriage is when you shack up and have sex, then a marriage ceremony (whether or not it involves a preacher, government paperwork, a big sit-down meal or whatever) is simply a celebration of something else. Something that is either about to happen that evening, or in many cases something that actually happened some time ago... It's great to have a celebration, but it doesn't make you married. If a monogamous couple shack up and never get around to having a wedding with a preacher and government paperwork, are they married or not? Clearly they are married, whether or not they recognise that themselves, as they've still done exactly what Adam and Eve did.
3) The most detailed description of a Biblical marriage that I can think of is actually in the Apocrypha, Tobit 6:10-8:9 (link below). It is very interesting reading. Note that this is a very unusual tale, and by quoting this I am not making any comment as to whether the spiritual elements of this account are actually valid or not (the canonicity of the book of Tobit is way off-topic), this is just a very detailed description of an ancient Hebrew marriage so well worth reading. In essence, Tobias turns up at Raguel's place, asks to marry his daughter, Raguel agrees, takes a blank piece of paper and writes up a marriage contract on the spot, they have tea, tell Tobias he'll find his wife in her bedroom, he goes to her, prays with her, sleeps with her, and they're married. Simple. And given that this is a very detailed, 2 chapter long description of what happened, it is particularly noteworthy that the one thing they DIDN'T do was send for a priest!
http://ebible.org/bible/kjv/Tobit.htm