In a 9 year old Lab it could be several different things!
First , a splinter is definitely possible. It can be very difficult to find one if it has penetrated deep, but doing a very careful inspection of the area between the toes and the pads should be done. IF you find a suspicious area of redness or swelling, you can try soaking the entire paw in warm water with Epsom salts for 5-10 minutes 2-3 times a day to try and draw the splinter out.
Next, one must consider the possiblity of some type of musculoskeletal injury. In large breeds, like Labs, this can vary from a ruptured Anterior Cruciate Ligament (ACL)in the knee joint to the development of degenerative joint disease, especially in the hips and the knees (stifles). Many of these disease processes usually have been present for a while and you don't notice anything until your pet stresses the joint and cannot compensate any longer. Labs also can develop a condition called LumboSacral Syndrome where the nerves from the lower lumbar area become inflamed and irritated due to spinal arthritis (spondylosis) and cause rear leg lameness and nerve deficits.
If the lameness persists for more than 2-3 days, than you should definitely have your pet checked out by your vet! He/She will likely do a thorough orthopedic exam and may suggest that radiographs of your pet's knees, hips, and lumbar spine be performed.
In the interim, you may use an adult strength aspirin (325 mg) every 6-8 hours WITH FOOD until you can get into the vet. IF your pet has any history of pancreatitis, upset stomach, or kidney disease, than you should just be safe and wait til your vet can prescribe you something made for your pet's needs. Aspirin can be irritating to the stomach lining, so it must be fed with meals. You cannot give your pet Acetaminophen (Tylenol), Ibuprofen, or any other OTC pain med without direct permission from your vet!!
It would be a good idea to rest your pet for the weekend. No stairs, no jumping, leash walks only and no rough play until you can get in for your vet appointment.
Hope this information was helpful to you! And I hope it's just a splinter :)
Best wishes,
Dr. Smith