I've written two songs that I actually have a beat to and I'm very proud of them but I'd like to get them copyrighted so that maybe I could sing them at contests without worry of them getting stolen considering that one is one I wrote about my boyfriend.

From everything that I read, your work is automatically protected in the United States under the current copyright laws once you have placed it in some sort of tangible form.

From the following site. U.S. Copyright Office - Copyright in General (FAQ)

When is my work protected?
Your work is under copyright protection the moment it is created and fixed in a tangible form that it is perceptible either directly or with the aid of a machine or device.

Do I have to register with your office to be protected?
No. In general, registration is voluntary. Copyright exists from the moment the work is created. You will have to register, however, if you wish to bring a lawsuit for infringement of a U.S. work. See Circular 1, Copyright Basics, section “Copyright Registration.”

To create a date of creation simply write it and place it in the mail to yourself, this will create a date stamp by the US postal service. Do not open it but put it in a safe place. If you need to protect your copyright after that, simply take the sealed letter to an attoreny and have it verified in the present of witnesses when they open it.