Sometimes hydrocodone can cause a lot of itching - but if you are used to taking it, you may know if this increased reaction could be due to it.
If the itching is similar to what you had before you started taking the cough syrup and other mediations, I would suggest for at night that you take a small dose of benadryl (25 or 50 mg) since it can be a little sedating, unless you have ever had a problem with it (which would be quite unusual). I almost wonder if your doctor missed giving you one - but steroids often take care of the itching so he may have neglected this on purpose.
You could also try apply benadryl topical cream. There is allergy medicine over the counter called Zyrtec, that can be given for allergies in the day time that is non drowsy - if your itching is bad during the day - read the label though first, it may have slightly stimulating qualities so it may not go well with some of your asthma medications or may actually increase their effect.
Other things to do for itching skin is an warm bath or soak of the areas in Aveeno (collodial oatmeal). You can make your own by putting plain oatmeal (old fashioned type is best) in a blender with water. Pour this into a stocking and then squeeze as needed to add to water. This is hydrating to the skin and also relieves itching well in most cases.
It will be important to try to discover what may be causing this reaction. Consider if there were any new medications, supplements, foods, soaps, etc. that were started before this occurred.
If their is not improvement you may want to go to urgent care clinic tomorrow. If not bothersome but still present Monday you will also want to notify your physician.
Hopefully the benadryl or collodial oatmeal will help.
If you have any questions or comments, please reply.