Curing Side Effects from Chemical Peel?

Dear Golda
Itchy is a good sign that your are allergic to something you are using on the skin. You can develop an allergy to virturally anything at any time. Think about what you are using on your skin. One of these products is most likely causing the problem.
Some products are more likely to be causing the issue. The steroid cream can help reduce inflammation but too much of a strong steroid product can damage the skin.
Steroids are no substitute for figuring out what is causing the problem. I recommend that if your current doctor has not stopped everything you are using on the skin, you might try this.
Reintroduce products one at a time. Consider getting a second opinion with a cosmetic dermatologist if things don't quickly settle down.

It is important to determine whether this is the beginning of a hypertrophic scarring process or simple allergic dermatitis. Also, do you have any fever blisters anywhere?
Skin undergoing deeper peels must be watched very closely for reddish raised spider web type changes that could convert to superficial scars. But, we have no photo and certainly cannot examine you. We don't know what kind of skin you have; and we don't know what your "medium plus chemical peel" really was; phenol, TCA, percentages, additives, etc.?
Allergic dermatitis requires treatment also, but again, that cannot be diagnosed with absolute certainty over the Internet.
Deeper peels are the ones that usually need close evaluation for the potential scarring. Having said that, even TCA peels over 35% (considered medium by many) can cause some real problems in certain patients.
It is very easy to second guess other doctors, so none of the Internet answers are going to be good enough in my opinion. Hopefully your doctor is a trained expert in peeling. Talk to him/her. If you seek a second opinion, find someone with extensive training and experience in peeling. A diploma, board certification, etc. does not guarantee your doctor had extensive residency or fellowship training in peeling.

From what you are describing you are having an allergic reaction. Steroids would be the treatment. :However, Dermovate is a super potent steroid so you must be very cautious when using it on the face.
You should obviously stop using any other topicals on your face. If you are not doing significantly better in a few days, an allergy to an ingredient which is common to Dermovate and the product you are allergic too must be considered. ( For that reason my own choice would be Synalar Ointment). I would also consider oral steroids since it sounds like you are having somewhat of a local hive-like reaction.
I agree with Dr. Steinsapir that if you are not doing better you should consult with a dermatologist. My preference would be a medical dermatologist who says allergic reactions all day long than a cosmetic dermatologist. You might need patch testing to help your dermatologist figure out what you are allergic to.
Good luck and I am sure your reaction will go away soon.