Yes they could!
Antibiotics are a life saver, but they can raise havoc with the gastrointestinal system.
Please try supplementing your dog's diet with two weeks of Prostora, which is a prescription probiotic available at most veterinarian offices. If your vet doesn't carry Prostora you can substitute an over the counter probiotic, such as Culterelle brand, or a good pediatric health food store brand. The yogurt, Activia has live probiotics and may be effective.
If the shivering is unrelated to the antibiotics, it could also be due to pain, such as spinal pain from disc disease.