You don't have to go if you don't want to--depending on what you told the person who invited you. And even if you already said you'd attend--when you were asked last-minute and put on the spot--you might be able to contact her and apologize and say that when you checked your schedule you realized you were already booked, or that you aren't feeling well and don't want to spread any germs, or something like that. I wouldn't make a habit of going back on RSVPs, but sometimes with casual events you can get away with it. It seems like the suddenness of it is giving you a lot of stress and I'm sure that's not what your aunt or the organizer of the party would want, so maybe it would be better to stay home than to go if you feel ill (heartburn) and tense. Maybe make an effort to get together with your aunt at a later time instead.
If you decide to go--depending on the gas station in your town, you might be able to pick up a decent token gift there. Seriously, if it's like a mini-convenience store, they might have gift cards to chain stores, flowers, boxed chocolates. Or just go with the birthday card, maybe write something nice inside of it. Definitely don't make excuses for not having a gift/different kind of gift, as that will only draw attention to it. I think at adult birthday parties gifts are optional, so it's not like you're doing something wrong by not having one.