Itching near the inner corner of the eye, close to the nose, for a short duration, is commonly caused by mild allergy, irritation from dust, dryness, sweating, rubbing, or minor blockage or irritation near the tear duct area. Since you do not have redness, swelling, discharge, pain, or vision problems, the condition may be mild and not serious. Frequent rubbing can further irritate the delicate skin around the eye and may worsen the itching, so try to avoid touching or rubbing the area as much as possible. Washing the eyes gently with clean water and using cold compresses may help reduce irritation. Lubricating or artificial tear eye drops are usually considered safe during breastfeeding and may help if the itching is related to dryness or mild irritation. However, avoid using antibiotic or steroid eye drops without medical advice because unnecessary use may cause side effects or worsen some eye conditions. Maintaining hand hygiene and avoiding dust, smoke, or cosmetic products near the eyes may also help. Since you are breastfeeding your 10-month-old baby, it is always best to use medicines only when really needed and preferably after medical advice. You should consult an eye doctor if the itching increases, redness develops, discharge appears, swelling occurs, vision becomes blurry, or the symptoms continue beyond a few days. Proper examination can help identify whether the cause is allergy, dryness, infection, or another minor eye condition and ensure safe treatment during breastfeeding.