Is it normal for the skin around my eyes to be itchy?

NO: Itching is usually a sign of allergy. This may be due to environmental factors or occasionally irritation from a chronically tearing eye. Best to make a list of all the things you use on your skin and see your ophthalmologist for a systematic treatment plan and identification of the allergens. Also may be due to dry eyes and eczema.

Not really: There are a lot of possible reasons for this, and it's worth getting evaluated. The most benign reasons are seasonal allergies and contact dermatitis (for example, a reaction to eyeliner). It can also be a sign of a larger skin problem (psoriasis, for example) or more rarely a disease affecting the autoimmune system in a broader way.

The most common: The most common cause of itching is blepharitis, which is inflammation of the eyelash base and eyelids. It is the most common problem seen in a general eye doctors office. Can be caused by allergies, bacteria, or associated with skin conditions such as psoriasis, rosacea, or eczema. Lid scrubs with dilute baby shampoo is the best treatment.