Are your tear ducts connected to nose?

Yes, the tear ducts are connected to the nose.

Tears are produced by the lacrimal glands, which are located above each eye. The tears then flow over the surface of the eye and into the puncta, which are small openings in the inner corners of the eyelids. The puncta drain the tears into the lacrimal sac, which is a small sac located in the bridge of the nose. From the lacrimal sac, the tears flow into the nasolacrimal duct, which is a small tube that connects the lacrimal sac to the nose. The tears then drain out of the nose through the nostrils.