Do the pain reliever creams or oils, that you can put on the outside of a swollen sprained joint, actually help the healing at all?

Depends on the cause. Your pain could be as a result of many different things. A thorough history and physical exam and possibly some laboratory and radiology exams are needed to determine the exact cause. Causes of pain may include: trauma (fracture, sprain, arthritis), infection, metabolic conditions (gout), musculoskeletal or biomechanical abnormality and neurologic conditions (neuropathy).
Pain relief. Most topical agents contain an analgesic like Aspirin or menthol and an anti-inflammatory agent like Aspirin again and arnica. These will help the discomfort but don't actually aid healing per say.
Topical analgesics. Topical creams for pain usually use menthol as a distractant which overrides the pain sensations. This does not directly improve healing, but can allow you to return to activity sooner. Continued, albeit reduced, activity improves muscle flexibility, lymphatic drainage, and blood flow, aiding in the healing process.
Depends on the cream. This really depends on the cream - if it is an icy hot-type cream, it may help symptoms but not relieve the underlying inflammation. There are a few prescription creams that actually contain the powerful anti-inflammatories that can attack the root of the problem.