I'm not sure, without seeing Lily, why her breathing is so elevated, whether it is pain, infection, or another trauma related incident. The antibiotic injection may help, or she may need further care, as she did go through a very traumatic event. If her breathing has not improved over the next 12-24 hours, it would be best to have a recheck for her - she may need tonging care until all of this is resolved.
Thank you for your email. Since Tortie was just seen by your veterinarian and was deemed healthy, her periodic bouts of rapid breathing may be normal, and may follow bouts of exertion or anxiety. If the periods that she is breathing rapidly become more frequent, or more severe, it would be a good idea to have her seen by your veterinarian and examined to make sure that she is okay. It might be helpful to video the episode, since she doesn't seem to breathe that way when she is at an appointment. I hope that she is okay!
Rapid breathing (tachypnea) is a respiratory disorder characterised by abnormal breathing that is rapid and shallow. It is caused by a reduced level of oxygen, mechanical disorders (where the lungs aren’t able to expand as they should, usually due to a build-up of fluid in or around the lungs), and physiological disorders in which the cat’s respiratory centre in the brain is over stimulated.