Events like weddings can be either "assigned" or "open" seating, and you haven't specified which this is.
Assigned seating events are those where the host have precisely determined exactly how many people are coming and have to pay for a dinner for each, whether or not they show up. These usually have guests seated at specific tables, so adding another guests can mean shuffling around everyone else to make sure everyone is seated, and also seated where they should be.
Open seating is less formal, and there should be plenty of seating for everyone.
Guests are meant to find their own seats, and will often serve themselves from a buffet table. With open seating adding a few more people is usually fairly trivial -- the list isn't "set" so it's assumed that single guests may bring a "plus one".
So it depends. If this is a formal event where the guest list was decided months ago, then you may ask, but be prepared to have your relations say "no" -- not because they want to be mean, but because it might mean uninviting another guest (which should be avoided).
On the other hand, if it's an open event (not atypical with large families where they're never sure exactly who might show up, and they wouldn't want to offend some distant relation) they should be more flexible.
I agree with the other answer that calling them is probably best, especially since time is short. If they're busy with the wedding arrangements, a text or email can be overlooked. It can be simple yet diplomatic, something like:
Hi cousin! Congratulations on your upcoming nuptials! I know this is last-minute but I was hoping to bring my girlfriend to your wedding so she can meet the whole family. I understand completely if this would be an inconvenience, of course, but I just wanted to check if it was possible.
Asking "is this possible" gives them an easy way to say "no", if it would be too much trouble. It also gives them an easy way to say "yes", as they may be enthusiastic about meeting your girlfriend, and it's always nice to have more people come to this kind of celebration.