Hello Sue, I'm Dr. Deb.
I recently came online and see that your question about Lily hasn't been answered. I'm so sorry that you've had to wait for a response,but if you still need assistance, I'd like to help if I can.
While most dogs tolerate steroids very well, the symptoms of panting and increased respiratory rate can be seen as a side effect of this drug. However, having said that, I would have expected Lily to have shown these signs after she received her first injection if she were going to react at all.
But, not all dogs read the textbooks so it's possible that this drug is responsible for her behavior although there are other possible explanations as well:
Pain, fever, anxiety, fear...these can also cause the signs you're seeing.
It should be relatively easy enough to take her temperature if you have a thermometer. Normal is between 100 and 102. 5 Fahrenheit.
If she hadn't been given a steroid shot, I might have suggested Aspirin (which could help with a fever or even pain); however, this drug would be contraindicated in this situation since to give it to her could increase the risk of gastric ulceration..the last thing I'd want to do.
Depending on whether or not this was a long or short acting steroid and if her symptoms are drug related, then she might behave this way for 24 hours or 72 hours or even longer, unfortunately. Oral steroids may be a more acceptable option for her in the future since you can modify the dose should side effects occur.
I hope this helps although, again, I'm sorry for the delayed response. Deb