My child has pinkish colored circles under her eyes could this be allergies? We have 2 dogs and 2 cats in our home

Allergic shiners? A pink or purple discoloration under the eyes due to allergies are called "allergic shiners." in a child who also has nasal congestion or runny nose likely has allergies. Since there are many indoor allergens other than your pets that could be triggering the symptoms, it would be best to get your child allergy tested to find the exact cause.
Yes. Most times these are known as "allergic shiners" because of chronic inflammation in the sinus passages. It might not necessarily be due to the cat/dog, but could also be due to the pollens they bring into the house if they are in and out. Also remember that mold and dust mites can also be allergens. See an allergist to get the little one tested.