First of all congratulations. 5 months? How are you holding up? Morning sickness is past for you or you are sensitive and you still have problems?
Did you get a lot of weight or you are still managing to keep it under the control?
About your question I think that as your doctor already mentioned cortisone injection are safe for you although you are pregnant. But if you feel that this is something you shouldn’t do than wait. Also you can seek another opinion and I think on a medical opinion. Go visit another doctor and check all the possibilities. I have read about this shoots and it seems to me that they are pretty safe but why risk health of your child if there is no need.
Please let us know how everything end up and what the name of your baby is. Share your experience with us.