Rimadyl is a nonsteroidal anti-inflammatory. These type of medications work better for muscle or tendon injuries including bruises, sprains, strains or pulled muscles. It is the same as giving a person motrin (advil), naproxen (aleve), or meloxicam (Mobic) or metacam to a bird. There does not need to be visible swelling for them to be effective and inflammation can be internal (and microscopic) and have NO visible or palpable signs. Just like if you overexert yourself or have muscle pain when starting an exercise program.
An example of this is pleurisy. It is an inflammation of the lining of the lung. There are no visible signs. Just chest pain particularly when breathing. It also doesn't usually show up in an Xray. With pleurisy you can throw Tramadol and all kinds of narcotics at it and patients get little or no relief. Give them and Asprin or Motrin and WOW the pain is gone or signficantly reduced. Inflamation needs an anti-inflamatory for best results.
If you are not confortable with Rimadyl ask if there is a different anti-inflammatory they can give to dogs.
(advise given from an ER/ICU nurse perspective)