Traditionally, if it says only YOUR name on the invite, only YOU are invited.
Unless she or the wedding party have told you otherwise despite how the invite was addressed, you should NOT bring a guest.
Many people go to weddings on their own. I have in the past. Have you not heard of "singles tables" where you get to meet other singles at the wedding?
You will be focusing on your friend and her big day, not how awkward you feel because you have to sit next to a guy you don't know for 3 hours. Big deal.
I do have to say that I am allowing my guests to bring dates, but I am having a formal wedding and have budgeted for that. Not everyone can afford that, nor should you expect them to. No one should be forced to pay for a guest's random friend they don't even know. Yes, you may be able to "get away" with it, but that doesn't justify the cost for her.
Go have a good time solo, and celebrate with your friend. If you absolutely cannot stand to go to a social event by yourself for a few hours, then fine, ask her if you can bring a date. If you and her are close, she might agree and not mind. Perhaps she simply assumed you had no one to bring (i.e. You ARE single). Perhaps she put you at the singles table so you can meet her "hot" single cousin. Perhaps she thinks you two have mutual friends that will also be there for you to hang out with. I would bring this up with HER, but don't just bring a "surprise" guest.
P.S. I'm not saying I disagree with you, just that you need to ask HER for permission, since it's HER wedding. Most people, myself included, have realized people in your situation and have allowed ALL guests to bring a date. However, there is probably a REASON why she has decided against this, most likely that she can't afford it. You really should ask her directly. It's only right.
Avis did make a very good point that it might make her feel awkward if you ask. That is true, which is why I said only ask her if you are *close* friends. You could say something like:
"Do you have a set number of seats already mapped out? The RSVP card doesn't indicate if it's OK for me to bring a guest or not, so I just thought I'd ask". If she doesn't want extra people, she can nicely say that "her seating plan is full". Give her an out. If you were planning on bringing a guest anyway no matter what, asking this isn't any worse in my opinion, but each case is individual.