thanks for the additional information and the picture. It doesn't appear that there is any swelling. It is possible that he has injured his back or has a problem with an invertebral disc. An intervertebral disc that has slipped or ruptured up into the spinal canal causes inflammation of the spinal cord, which in severe cases causes paralyses of the rear legs. In other cases, it just makes the dog have pain when they move in certain ways or stress is put on the discs. You can read about this here:
Dogs with a disc problem frequently stop jumping an often avoid stairs. In addition, when you pick up a dog under the arms, his whole weight ends up hanging and an enormous amount of pressure is put on the discs in the back. The proper way to pick up a dog is to put your hand on the chest between the front legs and scoop up the rear legs in the other hand and lift up keeping the spine horiontal.
Buffered aspirin can be given to a dog with a dosage of up to 5-10 mg per pound every 12 hours. Keep in mind that a dog's body does not metabolize aspirin in the same way as a human and thus should not be given more than a day or two without contacting your Vet. The aspirin may need to clear your dog’s system before other medications can be given, so keep that in mind if you decide to give aspirin and be sure and tell your vet when your dog is seen. Read side effects and precautions here.
Boston Terriers are prone to disc issues so he may have injured it in the fall. Your vet may need special imaging to rule out a disc injury. If it is a disc injury or your vet decides to treat without imaging with an anti-inflammatory medication, be sure to keep him crated so he is kept inactive. Only allow him out of the crate to eliminate and only on a leash. He may feel like he is healed but he needs about 7 days of inactivity to allow healing to get a good head start. Too much activity and he may reinjure himself with normal movement.
I'd go ahead and have him seen tomorrow so you know positively. If you decide to forgo a vet visit, then you might use aspirin for a day or two and stop for a few days keeping him totally inactive to see if there is improvement. Disc problems are best treated early though for the best chance of recovery.
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