yes you can. however, you need to try some other solutions first. adding fish oil to their diet, oatmeal baths, etc. I had to use cortisone as a last resort for my dog. But it helped immensley!
Dogs often have a variety things that they may be allergic to. While there are cortisone shots available to dogs with severe allergies, a veterinarian should always eb the one to oversee and or administer a powerful drug. Your veterinarian will do a simple physical exam to determine if the shots are needed.
Giving a cortisone shot is only going to relieve itching for a little while. Between you and your vet you will need to find out what allergies are coming from.
For allergies in dogs the cortisone could be given as steriods to suppress the allergic symptoms temporarily but it would be effective for two months only.