If it is formulated for dogs it should be safe to apply per the instructions. Does it say to keep them from licking the area? If course, it is better they not lick medicines.
You need to try to figure out what is causing the itching. Is it just in those areas or anywhere else? Food is always the first suspect. You might try a food with no grains, especially corn. You might try another protein source. If you are feeding a food with chicken, try gradually switching over to beef, lamb, duck or fish.
What you might try is washing the area with a diluted solution of Apple cider vinegar and water and dry thoroughly.
Good luck and please come back to update.
Also, hydrocortisone acetate is listed as the active ingredient which is equivalent to 0.5 hydrocortisone. So I was wondering is it alright if my dog were to lick it? Would there be any side effect or something like that?
If formulated for dogs it should be fine, work? time will tell. go light to see if there is any bad effects.
Does the dog smell .. may be a dermatitis, yeast if skin is dark, just a guess on what to loo for, what breed?