Recently eye looks crossed/lazy in pictures, could it be swollen tear duct?

Crossed eyes. If you have no known history of crossed or lazy eyes it would be unusual to develop crossed eyes without also noticing double vision. If your tear duct is swollen, it can cause the eyelid to be swollen. Be sure and see an ophthalmologist about this.
Eyes that are. Misaligned can either be due to something as benign as a refractive error which can be corrected by spectacles. Small angle deviations without double vision is usually not serious. Misalignment can also be due to other causes that may be serious and needs to be evaluated by your ophthalmologist. A complete exam will evaluate wether it is a muscular or neurological issue that needs attention.