Allergy or other. Red patches on your face could be due to an allergy to something you ate or something you put on your face, but could also be due to a lot of other causes such as acne or rosacea or other forms of dermatitis.
Difficult to answer. Without being able to see the rash and get more details, it is impossible to say. Allergies may be a possible cause, but I would recommend seeing your physician.
If they itch, yes. Shampoos contain botanical extracts. If you have weed pollen or fruit allergies you may react to one of these "natural" products. The hallmark of an allergic skin reaction is itching.