Hi there and thanks for your question. Sorry to hear that your dog is not well!
While I can't say for sure what is going on with your dog, what you have described certainly sounds like something called an aural hematoma.
Often we can't find the cause of an aural hematoma, but sometimes it can be there because the dog has been shaking her head because of an ear infection.
The swelling is actually a collection of blood that forms between the skin and the cartilage of the ear. This is actually quite a painful thing to have.
The next question is what to do. Really, she does need to see the vet. Dogs who are not treated for this will eventually have the swelling go down, but we will end up with quite severe scarring on the ear. Also, it may take some time and she will be in pain for most of this time.
Most vets treat this by doing surgery to remove the fluid and then suture the skin to the cartilage in several spots so there is no chance for fluid to accumulate again. However, some vets (including myself) are finding that these hematomas will often resolve when the dog is given oral steroids. This is much less expensive and seems to work fairly quickly. You can talk to your vet about all of the options.
This is really crummy because there is not much that I can recommend for you that will give her relief without a vet visit.
The only over the counter pain reliever that I ever recommend is aspirin. However, one of the main negative effects of aspirin is that it can cause an increase in bleeding. As your dog likely has a collection of blood in the ear, if we give aspirin we could actually make the hematoma worse!
The ear medication that you have may add some slight relief, but only if there is an underlying infection.
If you do decide to go to emergency, you can tell them that you are not interested in having surgery, but ask if they could prescribe either some prednisone (steroid), or at least another pain reliever until you can get to your regular vet.
The Rimadyl is a good idea!
If anything, if she will allow a cold compress (i.e. frozen peas) this may help. A hot compress will open up the blood vessels more and may contribute to more bleeding, but cold will help with the swelling. However, most dogs would not allow us to do this!