What is the name of the tear collecting structure under the skin near the bridge of the nose?

The name of the tear collecting structure under the skin near the bridge of the nose is the lacrimal sac. The lacrimal sac is part of the lacrimal drainage system or the lacrimal apparatus. The tears are produced in the lacrimal gland and will drain through a hole near the lower palpebral conjuntiva called the puncta which serves as the entrance in the lacrimal system. The tears will now enter the canalicula which serves as the passage way from the puncta to the lacrimal sac. Lastly, the tears in the lacrimal sac will drain to the nasolacrimal duct and to the nose. This also explains why we get runny nose when we are crying.